{ "cells": [ { "cell_type": "markdown", "id": "30fd42cd-bf60-4187-9150-50cd16340b2d", "metadata": {}, "source": [ "# Panel Data Analysis – Guns Dataset\n", "\n", "
\n", "\n", "בחלק זה נבצע ניתוח נתוני פאנל באמצעות מודלי\n", "Fixed Effects (FE)\n", "ו-Random Effects (RE).\n", "\n", "מטרת הניתוח היא לבחון את הקשר בין שיעור הפשיעה האלימה במדינות ארה\"ב לבין משתנים דמוגרפיים, כלכליים ומשתני מדיניות לאורך זמן, ולבחור בין שני המודלים באמצעות מבחן\n", "Hausman.\n", "\n", "לאחר בחירת המודל נבחן את שאריותיו ונבדוק האם קיימות בעיות במפרט המודל.\n", "\n", "
" ] }, { "cell_type": "code", "execution_count": 4, "id": "2daa76ba-6c42-4671-804b-6e1b196178d6", "metadata": { "vscode": { "languageId": "r" } }, "outputs": [], "source": [ "# Packages\n", "\n", "library(AER)\n", "library(plm)\n", "library(corrplot)\n", "library(lmtest)\n", "library(tseries)\n", "library(nlme)" ] }, { "cell_type": "code", "execution_count": 6, "id": "abaf083d-cf02-4713-ab2c-773336e17b7f", "metadata": { "vscode": { "languageId": "r" } }, "outputs": [], "source": [ "# Load the dataset\n", "\n", "data(\"Guns\", package = \"AER\")\n", "\n", "guns <- Guns" ] }, { "cell_type": "markdown", "id": "f78952f5-0f11-4b0f-ba4e-3fa5e556eeee", "metadata": {}, "source": [ "## 1. Data Description\n", "\n", "
\n", "\n", "הניתוח מבוסס על מאגר הנתונים\n", "Guns\n", "מספריית\n", "AER\n", "ב-R.\n", "\n", "זהו מאגר נתוני פאנל המתאר את 50 מדינות ארה\"ב ואת מחוז קולומביה לאורך השנים 1977–1999. כל תצפית מייצגת מדינה מסוימת בשנה מסוימת.\n", "\n", "המשתנה המוסבר בניתוח הוא\n", "violent,\n", "המייצג את שיעור מקרי הפשיעה האלימה ל-100,000 תושבים. מטרת הניתוח היא לבחון כיצד שיעור זה קשור למאפיינים דמוגרפיים וכלכליים של המדינה ולמשתנה\n", "law,\n", "המציין האם חוק\n", "Shall-Carry\n", "היה בתוקף במדינה באותה שנה.\n", "\n", "המשתנים במאגר הם:\n", "\n", "- state – המדינה.\n", "- year – שנת התצפית.\n", "- violent – שיעור מקרי פשיעה אלימה ל-100,000 תושבים.\n", "- murder – שיעור מקרי רצח ל-100,000 תושבים.\n", "- robbery – שיעור מקרי שוד ל-100,000 תושבים.\n", "- prisoners – שיעור האסירים שנידונו למאסר ל-100,000 תושבים, בשנה הקודמת.\n", "- afam – אחוז האוכלוסייה האפרו-אמריקאית בגילאי 10–64.\n", "- cauc – אחוז האוכלוסייה הקווקזית בגילאי 10–64.\n", "- male – אחוז הגברים בגילאי 10–29.\n", "- population – אוכלוסיית המדינה, במיליוני תושבים.\n", "- income – הכנסה אישית ריאלית לנפש.\n", "- density – צפיפות אוכלוסייה לשטח.\n", "- law – האם חוק Shall-Carry היה בתוקף במדינה ובשנה הנתונה.\n", "\n", "
" ] }, { "cell_type": "code", "execution_count": 9, "id": "6892bc89-bcff-42dc-b884-d71e9be44996", "metadata": { "vscode": { "languageId": "r" } }, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\t\n", "\t\n", "\n", "\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\n", "
A data.frame: 6 × 13
yearviolentmurderrobberyprisonersafamcaucmalepopulationincomedensitystatelaw
<fct><dbl><dbl><dbl><int><dbl><dbl><dbl><dbl><dbl><dbl><fct><fct>
11977414.414.2 96.8 838.38487355.1229118.174413.7804039563.1480.0745524Alabamano
21978419.113.3 99.1 948.35210155.1436717.994083.8318389932.0000.0755667Alabamano
31979413.313.2109.51448.32957555.1358617.839343.8662489877.0280.0762453Alabamano
41980448.513.2132.11418.40838654.9125917.734203.9003689541.4280.0768288Alabamano
51981470.511.9126.51498.48343554.9251317.673723.9185319548.3510.0771866Alabamano
61982447.710.6112.01838.51400054.8962117.510523.9252299478.9190.0773185Alabamano
\n" ], "text/latex": [ "A data.frame: 6 × 13\n", "\\begin{tabular}{r|lllllllllllll}\n", " & year & violent & murder & robbery & prisoners & afam & cauc & male & population & income & density & state & law\\\\\n", " & & & & & & & & & & & & & \\\\\n", "\\hline\n", "\t1 & 1977 & 414.4 & 14.2 & 96.8 & 83 & 8.384873 & 55.12291 & 18.17441 & 3.780403 & 9563.148 & 0.0745524 & Alabama & no\\\\\n", "\t2 & 1978 & 419.1 & 13.3 & 99.1 & 94 & 8.352101 & 55.14367 & 17.99408 & 3.831838 & 9932.000 & 0.0755667 & Alabama & no\\\\\n", "\t3 & 1979 & 413.3 & 13.2 & 109.5 & 144 & 8.329575 & 55.13586 & 17.83934 & 3.866248 & 9877.028 & 0.0762453 & Alabama & no\\\\\n", "\t4 & 1980 & 448.5 & 13.2 & 132.1 & 141 & 8.408386 & 54.91259 & 17.73420 & 3.900368 & 9541.428 & 0.0768288 & Alabama & no\\\\\n", "\t5 & 1981 & 470.5 & 11.9 & 126.5 & 149 & 8.483435 & 54.92513 & 17.67372 & 3.918531 & 9548.351 & 0.0771866 & Alabama & no\\\\\n", "\t6 & 1982 & 447.7 & 10.6 & 112.0 & 183 & 8.514000 & 54.89621 & 17.51052 & 3.925229 & 9478.919 & 0.0773185 & Alabama & no\\\\\n", "\\end{tabular}\n" ], "text/markdown": [ "\n", "A data.frame: 6 × 13\n", "\n", "| | year <fct> | violent <dbl> | murder <dbl> | robbery <dbl> | prisoners <int> | afam <dbl> | cauc <dbl> | male <dbl> | population <dbl> | income <dbl> | density <dbl> | state <fct> | law <fct> |\n", "|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n", "| 1 | 1977 | 414.4 | 14.2 | 96.8 | 83 | 8.384873 | 55.12291 | 18.17441 | 3.780403 | 9563.148 | 0.0745524 | Alabama | no |\n", "| 2 | 1978 | 419.1 | 13.3 | 99.1 | 94 | 8.352101 | 55.14367 | 17.99408 | 3.831838 | 9932.000 | 0.0755667 | Alabama | no |\n", "| 3 | 1979 | 413.3 | 13.2 | 109.5 | 144 | 8.329575 | 55.13586 | 17.83934 | 3.866248 | 9877.028 | 0.0762453 | Alabama | no |\n", "| 4 | 1980 | 448.5 | 13.2 | 132.1 | 141 | 8.408386 | 54.91259 | 17.73420 | 3.900368 | 9541.428 | 0.0768288 | Alabama | no |\n", "| 5 | 1981 | 470.5 | 11.9 | 126.5 | 149 | 8.483435 | 54.92513 | 17.67372 | 3.918531 | 9548.351 | 0.0771866 | Alabama | no |\n", "| 6 | 1982 | 447.7 | 10.6 | 112.0 | 183 | 8.514000 | 54.89621 | 17.51052 | 3.925229 | 9478.919 | 0.0773185 | Alabama | no |\n", "\n" ], "text/plain": [ " year violent murder robbery prisoners afam cauc male population\n", "1 1977 414.4 14.2 96.8 83 8.384873 55.12291 18.17441 3.780403 \n", "2 1978 419.1 13.3 99.1 94 8.352101 55.14367 17.99408 3.831838 \n", "3 1979 413.3 13.2 109.5 144 8.329575 55.13586 17.83934 3.866248 \n", "4 1980 448.5 13.2 132.1 141 8.408386 54.91259 17.73420 3.900368 \n", "5 1981 470.5 11.9 126.5 149 8.483435 54.92513 17.67372 3.918531 \n", "6 1982 447.7 10.6 112.0 183 8.514000 54.89621 17.51052 3.925229 \n", " income density state law\n", "1 9563.148 0.0745524 Alabama no \n", "2 9932.000 0.0755667 Alabama no \n", "3 9877.028 0.0762453 Alabama no \n", "4 9541.428 0.0768288 Alabama no \n", "5 9548.351 0.0771866 Alabama no \n", "6 9478.919 0.0773185 Alabama no " ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "'data.frame':\t1173 obs. of 13 variables:\n", " $ year : Factor w/ 23 levels \"1977\",\"1978\",..: 1 2 3 4 5 6 7 8 9 10 ...\n", " $ violent : num 414 419 413 448 470 ...\n", " $ murder : num 14.2 13.3 13.2 13.2 11.9 10.6 9.2 9.4 9.8 10.1 ...\n", " $ robbery : num 96.8 99.1 109.5 132.1 126.5 ...\n", " $ prisoners : int 83 94 144 141 149 183 215 243 256 267 ...\n", " $ afam : num 8.38 8.35 8.33 8.41 8.48 ...\n", " $ cauc : num 55.1 55.1 55.1 54.9 54.9 ...\n", " $ male : num 18.2 18 17.8 17.7 17.7 ...\n", " $ population: num 3.78 3.83 3.87 3.9 3.92 ...\n", " $ income : num 9563 9932 9877 9541 9548 ...\n", " $ density : num 0.0746 0.0756 0.0762 0.0768 0.0772 ...\n", " $ state : Factor w/ 51 levels \"Alabama\",\"Alaska\",..: 1 1 1 1 1 1 1 1 1 1 ...\n", " $ law : Factor w/ 2 levels \"no\",\"yes\": 1 1 1 1 1 1 1 1 1 1 ...\n" ] }, { "data": { "text/plain": [ " year violent murder robbery \n", " 1977 : 51 Min. : 47.0 Min. : 0.200 Min. : 6.4 \n", " 1978 : 51 1st Qu.: 283.1 1st Qu.: 3.700 1st Qu.: 71.1 \n", " 1979 : 51 Median : 443.0 Median : 6.400 Median : 124.1 \n", " 1980 : 51 Mean : 503.1 Mean : 7.665 Mean : 161.8 \n", " 1981 : 51 3rd Qu.: 650.9 3rd Qu.: 9.800 3rd Qu.: 192.7 \n", " 1982 : 51 Max. :2921.8 Max. :80.600 Max. :1635.1 \n", " (Other):867 \n", " prisoners afam cauc male \n", " Min. : 19.0 Min. : 0.2482 Min. :21.78 Min. :12.21 \n", " 1st Qu.: 114.0 1st Qu.: 2.2022 1st Qu.:59.94 1st Qu.:14.65 \n", " Median : 187.0 Median : 4.0262 Median :65.06 Median :15.90 \n", " Mean : 226.6 Mean : 5.3362 Mean :62.95 Mean :16.08 \n", " 3rd Qu.: 291.0 3rd Qu.: 6.8507 3rd Qu.:69.20 3rd Qu.:17.53 \n", " Max. :1913.0 Max. :26.9796 Max. :76.53 Max. :22.35 \n", " \n", " population income density state \n", " Min. : 0.4028 Min. : 8555 Min. :7.071e-04 Alabama : 23 \n", " 1st Qu.: 1.1877 1st Qu.:11935 1st Qu.:3.191e-02 Alaska : 23 \n", " Median : 3.2713 Median :13402 Median :8.157e-02 Arizona : 23 \n", " Mean : 4.8163 Mean :13725 Mean :3.520e-01 Arkansas : 23 \n", " 3rd Qu.: 5.6856 3rd Qu.:15271 3rd Qu.:1.777e-01 California: 23 \n", " Max. :33.1451 Max. :23647 Max. :1.110e+01 Colorado : 23 \n", " (Other) :1035 \n", " law \n", " no :888 \n", " yes:285 \n", " \n", " \n", " \n", " \n", " " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "\n", "
  1. 1173
  2. 13
\n" ], "text/latex": [ "\\begin{enumerate*}\n", "\\item 1173\n", "\\item 13\n", "\\end{enumerate*}\n" ], "text/markdown": [ "1. 1173\n", "2. 13\n", "\n", "\n" ], "text/plain": [ "[1] 1173 13" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Inspect the data\n", "\n", "head(guns)\n", "str(guns)\n", "summary(guns)\n", "dim(guns)" ] }, { "cell_type": "markdown", "id": "e12f0510-3bf9-40c7-b0d9-3e5b261ecc63", "metadata": {}, "source": [ "## 2. Data Preparation and Panel Structure\n", "\n", "
\n", "\n", "בשלב זה בחנו את מבנה מאגר הנתונים ואת הסטטיסטיקה התיאורית של המשתנים, ובדקנו האם קיימים ערכים חסרים.\n", "\n", "בנוסף, הגדרנו את\n", "state\n", "כממד הרוחבי ואת\n", "year\n", "כממד הזמן.\n", "\n", " במקרה שלנו, כל מדינה היא יחידה נפרדת וכל שנה היא תקופת זמן.\n", "\n", "\n", "המשתנה\n", "year\n", "כבר מוגדר במאגר כמשתנה מסוג\n", "factor\n", "בעל 23 רמות. לכן כאשר הוא נכלל במודל,\n", "R\n", "יוצר באופן אוטומטי משתני דמה לשנים, כאשר שנת 1977 משמשת כקטגוריית הבסיס.\n", "\n", "\n", "
" ] }, { "cell_type": "code", "execution_count": 12, "id": "f49fcf68-5119-476e-9d66-937b4103e2f9", "metadata": { "vscode": { "languageId": "r" } }, "outputs": [ { "data": { "text/html": [ "FALSE" ], "text/latex": [ "FALSE" ], "text/markdown": [ "FALSE" ], "text/plain": [ "[1] FALSE" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "
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\n", "\n", "המאגר כולל 1,173 תצפיות ו-13 משתנים, המתקבלים מ-51 מדינות הנצפות במשך 23 שנים.\n", "\n", "לא נמצאו ערכים חסרים במאגר.\n", "\n", "בנוסף, נמצא כי מדובר ב-\n", "Balanced Panel,\n", "כלומר לכל אחת מ-51 המדינות קיימת תצפית בכל אחת מ-23 השנים.\n", "\n", "לכן ניתן להמשיך לניתוח ללא צורך בהסרת תצפיות עקב ערכים חסרים או חוסר איזון במבנה הפאנל.\n", "\n", "
" ] }, { "cell_type": "markdown", "id": "fcfa3344-f98d-4134-9826-bfb16e0953b0", "metadata": {}, "source": [ "## 3. Exploratory Data Analysis\n", "\n", "
\n", "\n", "לפני הגדרת מודלי\n", "Fixed Effects\n", "ו-Random Effects,\n", "בחנו את ההתפלגויות של המשתנה המוסבר ושל המשתנים הרציפים שעשויים להיכלל במודל.\n", "\n", "מטרת הבדיקה היא לזהות משתנים בעלי התפלגות מוטה מאוד או פערים גדולים בסדרי הגודל, ולבחון האם טרנספורמציית\n", "log\n", "עשויה להתאים להם.\n", "\n", "בשלב זה איננו דורשים שהמשתנים המסבירים עצמם יתפלגו נורמלית. ההיסטוגרמות משמשות בעיקר לבחינת צורת ההתפלגות ולבחינת הצורך בטרנספורמציה.\n", "\n", "
" ] }, { "cell_type": "code", "execution_count": 16, "id": "e7a2560f-71e6-4815-8d1a-298c7800d2f5", "metadata": { "vscode": { "languageId": "r" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "Plot with title \"Income\"" ] }, "metadata": { "image/png": { "height": 720, "width": 960 } }, "output_type": "display_data" } ], "source": [ "options(repr.plot.width = 16, repr.plot.height = 12)\n", "par(mfrow = c(2, 2))\n", "\n", "hist(guns$violent,\n", " main = \"Violent Crime Rate\",\n", " xlab = \"violent\")\n", "\n", "hist(guns$prisoners,\n", " main = \"Prisoners\",\n", " xlab = \"prisoners\")\n", "\n", "hist(guns$population,\n", " main = \"Population\",\n", " xlab = \"population\")\n", "\n", "hist(guns$income,\n", " main = \"Income\",\n", " xlab = \"income\")\n", "\n", "par(mfrow = c(1, 1))" ] }, { "cell_type": "code", "execution_count": 27, "id": "0c6d5b48-202f-4492-b893-132c7ac24e67", "metadata": { "vscode": { "languageId": "r" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "Plot with title \"Young Male Population\"" ] }, "metadata": { "image/png": { "height": 720, "width": 960 } }, "output_type": "display_data" } ], "source": [ "options(repr.plot.width = 16, repr.plot.height = 12)\n", "par(mfrow = c(2, 2))\n", "\n", "hist(guns$density,\n", " main = \"Population Density\",\n", " xlab = \"density\")\n", "\n", "hist(guns$afam,\n", " main = \"African-American Population\",\n", " xlab = \"afam\")\n", "\n", "hist(guns$cauc,\n", " main = \"Caucasian Population\",\n", " xlab = \"cauc\")\n", "\n", "hist(guns$male,\n", " main = \"Young Male Population\",\n", " xlab = \"male\")\n", "\n", "par(mfrow = c(1, 1))" ] }, { "cell_type": "markdown", "id": "6861be47-7f05-4642-bcd7-22b5e15fcd20", "metadata": {}, "source": [ "## 4. Log Transformation\n", "\n", "
\n", "\n", "מההיסטוגרמות ניתן לראות כי\n", "violent,\n", "prisoners,\n", "population\n", "ו-density\n", "מאופיינים בהטיה משמעותית ימינה.\n", "\n", "לכן נבצע עבור משתנים אלה טרנספורמציית\n", "log.\n", "\n", "\n", "לבחירה זו יש שתי מטרות. מבחינה סטטיסטית, הלוגריתם מצמצם את השפעתם של ערכים גבוהים מאוד ומקרב את המשתנים לסקאלה מאוזנת יותר. מבחינה כלכלית, הוא גם מאפשר לפרש קשרים יחסיים, כאשר גם המשתנה המוסבר וגם מסביר מסוים נמצאים בלוגריתם, המקדם של אותו מסביר ניתן לפרש כגמישות בקירוב - אחוז השינוי ב-violent הקשור לעלייה של 1% במסביר, בהינתן יתר המשתנים.\n", "\n", "\n", "לאחר הטרנספורמציה נבחן מחדש את ההתפלגויות כדי לוודא שהשינוי אכן שיפר את צורתן.\n", "\n", "המשתנים\n", "income,\n", "afam,\n", "cauc\n", "ו-male\n", "יישארו בשלב זה בסקאלה המקורית, משום שלא נצפתה עבורם הטיה המצדיקה טרנספורמציה דומה.\n", "\n", "
" ] }, { "cell_type": "code", "execution_count": 30, "id": "e3ca8010-fe6f-4346-b102-79993f52df60", "metadata": { "vscode": { "languageId": "r" } }, "outputs": [], "source": [ "# Log transformations for right-skewed variables\n", "\n", "guns$log_violent <- log(guns$violent)\n", "guns$log_prisoners <- log(guns$prisoners)\n", "guns$log_population <- log(guns$population)\n", "guns$log_density <- log(guns$density)" ] }, { "cell_type": "code", "execution_count": 32, "id": "b67ab91f-d0d8-4e31-a800-ebcb63081289", "metadata": { "vscode": { "languageId": "r" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "Plot with title \"Log Population Density\"" ] }, "metadata": { "image/png": { "height": 720, "width": 960 } }, "output_type": "display_data" } ], "source": [ "options(repr.plot.width = 16, repr.plot.height = 12)\n", "\n", "par(mfrow = c(2, 2))\n", "\n", "hist(guns$log_violent,\n", " main = \"Log Violent Crime Rate\",\n", " xlab = \"log(violent)\")\n", "\n", "hist(guns$log_prisoners,\n", " main = \"Log Prisoners\",\n", " xlab = \"log(prisoners)\")\n", "\n", "hist(guns$log_population,\n", " main = \"Log Population\",\n", " xlab = \"log(population)\")\n", "\n", "hist(guns$log_density,\n", " main = \"Log Population Density\",\n", " xlab = \"log(density)\")\n", "\n", "par(mfrow = c(1, 1))" ] }, { "cell_type": "markdown", "id": "75183c67-2c51-4346-ab37-8ff4970ae315", "metadata": {}, "source": [ "
\n", "\n", "לאחר ביצוע טרנספורמציית\n", "log\n", "ניתן לראות שיפור ברור בהתפלגויות של ארבעת המשתנים.\n", "\n", "ההטיה החזקה ימינה של\n", "violent\n", "ו-prisoners\n", "הצטמצמה משמעותית, ושתי ההתפלגויות הפכו סימטריות יותר.\n", "\n", "גם עבור\n", "population\n", "ו-density\n", "הטרנספורמציה צמצמה באופן משמעותי את הפערים בין הערכים ואת ההטיה שנצפתה בנתונים המקוריים.\n", "\n", "לכן בהמשך הניתוח נשתמש ב-\n", "log(violent)\n", "כמשתנה המוסבר, וב-\n", "log(prisoners),\n", "log(population)\n", "ו-log(density)\n", "כגרסאות של המשתנים המסבירים המתאימים.\n", "\n", "
" ] }, { "cell_type": "markdown", "id": "f25c3604-df97-4be8-a048-dbc1d18cc0ca", "metadata": {}, "source": [ "## 5. Correlation and Multicollinearity\n", "\n", "
\n", "\n", "לפני הגדרת מודלי הפאנל נבחן את הקשרים בין המשתנים המסבירים הרציפים.\n", "\n", "מטרת הבדיקה היא לזהות זוגות של משתנים בעלי מתאם גבוה מאוד, אשר עלולים ליצור בעיית\n", "multicollinearity\n", "ולהקשות על הפרדת ההשפעה של כל אחד מהם במודל.\n", "\n", "המשתנים\n", "murder\n", "ו-robbery\n", "אינם נכללים כמסבירים, מכיוון שהם מתארים סוגים של פשיעה הנכללים במדד הפשיעה האלימה שאותו אנו מנסים להסביר.\n", "\n", "
" ] }, { "cell_type": "code", "execution_count": 36, "id": "6df975bc-2cd0-47cd-8660-19652ce0d701", "metadata": { "vscode": { "languageId": "r" } }, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\t\n", "\n", "\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\n", "
A matrix: 7 × 7 of type dbl
log_prisonersafamcaucmalelog_populationincomelog_density
log_prisoners 1.00 0.48-0.46-0.54 0.20 0.44 0.22
afam 0.48 1.00-0.98 0.02 0.03 0.26 0.41
cauc-0.46-0.98 1.00-0.01-0.05-0.19-0.42
male-0.54 0.02-0.01 1.00-0.15-0.53-0.24
log_population 0.20 0.03-0.05-0.15 1.00 0.11 0.43
income 0.44 0.26-0.19-0.53 0.11 1.00 0.38
log_density 0.22 0.41-0.42-0.24 0.43 0.38 1.00
\n" ], "text/latex": [ "A matrix: 7 × 7 of type dbl\n", "\\begin{tabular}{r|lllllll}\n", " & log\\_prisoners & afam & cauc & male & log\\_population & income & log\\_density\\\\\n", "\\hline\n", "\tlog\\_prisoners & 1.00 & 0.48 & -0.46 & -0.54 & 0.20 & 0.44 & 0.22\\\\\n", "\tafam & 0.48 & 1.00 & -0.98 & 0.02 & 0.03 & 0.26 & 0.41\\\\\n", "\tcauc & -0.46 & -0.98 & 1.00 & -0.01 & -0.05 & -0.19 & -0.42\\\\\n", "\tmale & -0.54 & 0.02 & -0.01 & 1.00 & -0.15 & -0.53 & -0.24\\\\\n", "\tlog\\_population & 0.20 & 0.03 & -0.05 & -0.15 & 1.00 & 0.11 & 0.43\\\\\n", "\tincome & 0.44 & 0.26 & -0.19 & -0.53 & 0.11 & 1.00 & 0.38\\\\\n", "\tlog\\_density & 0.22 & 0.41 & -0.42 & -0.24 & 0.43 & 0.38 & 1.00\\\\\n", "\\end{tabular}\n" ], "text/markdown": [ "\n", "A matrix: 7 × 7 of type dbl\n", "\n", "| | log_prisoners | afam | cauc | male | log_population | income | log_density |\n", "|---|---|---|---|---|---|---|---|\n", "| log_prisoners | 1.00 | 0.48 | -0.46 | -0.54 | 0.20 | 0.44 | 0.22 |\n", "| afam | 0.48 | 1.00 | -0.98 | 0.02 | 0.03 | 0.26 | 0.41 |\n", "| cauc | -0.46 | -0.98 | 1.00 | -0.01 | -0.05 | -0.19 | -0.42 |\n", "| male | -0.54 | 0.02 | -0.01 | 1.00 | -0.15 | -0.53 | -0.24 |\n", "| log_population | 0.20 | 0.03 | -0.05 | -0.15 | 1.00 | 0.11 | 0.43 |\n", "| income | 0.44 | 0.26 | -0.19 | -0.53 | 0.11 | 1.00 | 0.38 |\n", "| log_density | 0.22 | 0.41 | -0.42 | -0.24 | 0.43 | 0.38 | 1.00 |\n", "\n" ], "text/plain": [ " log_prisoners afam cauc male log_population income\n", "log_prisoners 1.00 0.48 -0.46 -0.54 0.20 0.44 \n", "afam 0.48 1.00 -0.98 0.02 0.03 0.26 \n", "cauc -0.46 -0.98 1.00 -0.01 -0.05 -0.19 \n", "male -0.54 0.02 -0.01 1.00 -0.15 -0.53 \n", "log_population 0.20 0.03 -0.05 -0.15 1.00 0.11 \n", "income 0.44 0.26 -0.19 -0.53 0.11 1.00 \n", "log_density 0.22 0.41 -0.42 -0.24 0.43 0.38 \n", " log_density\n", "log_prisoners 0.22 \n", "afam 0.41 \n", "cauc -0.42 \n", "male -0.24 \n", "log_population 0.43 \n", "income 0.38 \n", "log_density 1.00 " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Correlation matrix\n", "\n", "cor_data <- guns[, c(\n", " \"log_prisoners\",\n", " \"afam\",\n", " \"cauc\",\n", " \"male\",\n", " \"log_population\",\n", " \"income\",\n", " \"log_density\"\n", ")]\n", "\n", "cor_matrix <- cor(cor_data)\n", "\n", "round(cor_matrix, 2)" ] }, { "cell_type": "code", "execution_count": 38, "id": "8c6e2ea9-0ab4-4641-85ca-9ec4483ad0a0", "metadata": { "vscode": { "languageId": "r" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "Plot with title \"\"" ] }, "metadata": { "image/png": { "height": 720, "width": 840 } }, "output_type": "display_data" } ], "source": [ "options(repr.plot.width = 14, repr.plot.height = 12)\n", "\n", "corrplot(\n", " cor_matrix,\n", " method = \"number\",\n", " type = \"upper\",\n", " tl.cex = 1.1,\n", " number.cex = 1,\n", " number.digits = 2\n", ")" ] }, { "cell_type": "markdown", "id": "64f12f38-d388-4ee9-82cc-f1e567356ce9", "metadata": {}, "source": [ "
\n", "\n", "מטריצת המתאמים מצביעה על מתאם שלילי גבוה מאוד בין\n", "afam\n", "ל-cauc,\n", "כאשר מקדם המתאם הוא\n", "-0.98.\n", "\n", "כדי לשמור על מפרט חסכוני ולהימנע מ-\n", "multicollinearity\n", "נשאיר את\n", "afam\n", "כמשתנה המייצג היבט זה של ההרכב הדמוגרפי ונשמיט את\n", "cauc.\n", "הבחירה אינה טענה שלפיה אחד המשתנים חשוב כלכלית יותר מהשני, היא נועדה למנוע ייצוג כפול של מידע כמעט זהה.\n", "\n", "\n", "שאר המתאמים בין המשתנים המסבירים הם מתונים יותר, ולכן בשלב זה אין הצדקה להסיר משתנים נוספים על סמך מטריצת המתאמים בלבד.\n", "\n", "
" ] }, { "cell_type": "markdown", "id": "5402f9ef-6899-4fb4-8f5e-ce07906a6989", "metadata": {}, "source": [ "## 6. Model Specification\n", "\n", "
\n", "\n", "לאחר שלבי הכנת הנתונים, הטרנספורמציות ובדיקת המתאמים, נגדיר את המפרט הראשוני של מודלי הפאנל.\n", "\n", "המשתנה המוסבר הוא\n", "log_violent.\n", "\n", "המשתנים המסבירים כוללים את משתנה המדיניות\n", "law,\n", "את המשתנים הדמוגרפיים\n", "afam\n", "ו-male,\n", "את המשתנים הכלכליים והמבניים\n", "log_prisoners,\n", "log_population,\n", "income\n", "ו-log_density,\n", "וכן משתני שנה לצורך שליטה בשינויים משותפים לכל המדינות לאורך זמן.\n", "\n", "המשתנים\n", "murder\n", "ו-robbery\n", "אינם נכללים במודל משום שהם מתארים סוגי פשיעה הנכללים במדד\n", "violent\n", "שאותו אנו מנסים להסביר.\n", "\n", "המשתנה\n", "cauc\n", "אינו נכלל בעקבות המתאם הגבוה עם\n", "afam.\n", "\n", "
" ] }, { "cell_type": "markdown", "id": "6c00bb99-7b73-41ac-afac-e63e1aba1483", "metadata": {}, "source": [ "### Initial Model Equation\n", "\n", "
\n", "\n", "בהתאם לבחירת המשתנים ולטרנספורמציות שבוצעו, המפרט הראשוני של המודל הוא:\n", "\n", "
\n", "\n", "$$\n", "\\ln(violent_{it}) =\n", "\\alpha\n", "+ \\beta_1 law_{it}\n", "+ \\beta_2 \\ln(prisoners_{it})\n", "+ \\beta_3 afam_{it}\n", "+ \\beta_4 male_{it}\n", "+ \\beta_5 \\ln(population_{it})\n", "+ \\beta_6 income_{it}\n", "+ \\beta_7 \\ln(density_{it})\n", "+ \\sum_{t=1978}^{1999}\\gamma_t D_t\n", "+ \\varepsilon_{it}\n", "$$\n", "\n", "
\n", "\n", "כאשר:\n", "\n", "- $i$ מייצג מדינה.\n", "- $t$ מייצג שנה.\n", "- $violent_{it}$ הוא שיעור הפשיעה האלימה במדינה $i$ בשנה $t$.\n", "- $D_t$ הם משתני דמה לשנים, כאשר שנת 1977 משמשת כשנת הבסיס.\n", "- $\\beta_1,\\ldots,\\beta_7$ הם המקדמים של המשתנים המסבירים.\n", "- $\\gamma_t$ מייצגים את השפעות השנים.\n", "- $\\varepsilon_{it}$ הוא רכיב השגיאה.\n", "\n", "
" ] }, { "cell_type": "code", "execution_count": 43, "id": "5c07dc42-0156-47c2-bfb4-79fbb76ec802", "metadata": { "vscode": { "languageId": "r" } }, "outputs": [], "source": [ "# Initial panel model specification\n", "\n", "formula_initial <- log_violent ~\n", " law +\n", " log_prisoners +\n", " afam +\n", " male +\n", " log_population +\n", " income +\n", " log_density +\n", " year" ] }, { "cell_type": "markdown", "id": "4b5d765e-3385-48ee-af26-c30db1956ea6", "metadata": {}, "source": [ "## 7. Fixed Effects and Random Effects Models\n", "\n", "
\n", "\n", "כעת נאמוד את שני מודלי הפאנל על בסיס אותו מפרט ראשוני.\n", "\n", "מודל\n", "Fixed Effects (FE)\n", "מאפשר לאפקטים הבלתי נצפים והקבועים של כל מדינה להיות מתואמים עם המשתנים המסבירים. האמידה מבוססת על השינויים המתרחשים בתוך אותה מדינה לאורך זמן.\n", "\n", "מודל\n", "Random Effects (RE)\n", "מניח שהאפקט הייחודי של כל מדינה אינו מתואם עם המשתנים המסבירים.\n", "\n", "בשלב זה נאמוד את שני המודלים על אותו מפרט ונבחן את תוצאותיהם.\n", "\n", "אם תזוהה בעיה מבנית במפרט המשותף לשני המודלים, כגון\n", "multicollinearity\n", "חזקה, נטפל בה לפני ההשוואה.\n", "\n", "לאחר קביעת מפרט משותף תקין נשתמש במבחן\n", "Hausman\n", "לבחירה בין\n", "FE\n", "ל-RE.\n", "סינון המשתנים לפי רמת מובהקות יתבצע לאחר מכן במודל שנבחר.\n", "\n", "
\n" ] }, { "cell_type": "markdown", "id": "d7417b03-653a-49ed-8e90-8d5f5718288c", "metadata": {}, "source": [ "\n", "### Fixed Effects Model\n", "\n", "$$\n", "\\ln(violent_{it}) =\n", "\\alpha_i\n", "+ X_{it}'\\beta\n", "+ \\sum_{t=1978}^{1999}\\gamma_t D_t\n", "+ \\varepsilon_{it}\n", "$$\n", "\n", "
\n", "\n", "במודל\n", "Fixed Effects\n", "לכל מדינה קיים אפקט קבוע משלה,\n", "$\\alpha_i$.\n", "כך ניתן לשלוט במאפיינים בלתי נצפים של המדינה שאינם משתנים לאורך זמן, גם כאשר הם מתואמים עם המשתנים המסבירים.\n", "\n", "
\n", "\n", "### Random Effects Model\n", "\n", "$$\n", "\\ln(violent_{it}) =\n", "\\alpha\n", "+ X_{it}'\\beta\n", "+ \\sum_{t=1978}^{1999}\\gamma_t D_t\n", "+ \\mu_i\n", "+ \\varepsilon_{it}\n", "$$\n", "\n", "
\n", "\n", "במודל\n", "Random Effects\n", "ההבדל הייחודי בין המדינות מיוצג באמצעות\n", "$\\mu_i$,\n", "שהוא רכיב אקראי של המדינה.\n", "\n", "ההנחה המרכזית של מודל זה היא שהאפקט הייחודי למדינה אינו מתואם עם המשתנים המסבירים:\n", "\n", "
\n", "\n", "$$\n", "Cov(\\mu_i,X_{it})=0\n", "$$\n", "\n", "
\n", "\n", "מבחן\n", "Hausman\n", "ישמש בהמשך לבחינת התאמת הנחה זו ולבחירה בין שני המודלים.\n", "\n", "
" ] }, { "cell_type": "code", "execution_count": 47, "id": "5c65b7fa-561e-47d2-840d-a35fc443c288", "metadata": { "vscode": { "languageId": "r" } }, "outputs": [ { "data": { "text/plain": [ "Oneway (individual) effect Within Model\n", "\n", "Call:\n", "plm(formula = formula_initial, data = guns, model = \"within\", \n", " index = c(\"state\", \"year\"))\n", "\n", "Balanced Panel: n = 51, T = 23, N = 1173\n", "\n", "Residuals:\n", " Min. 1st Qu. Median 3rd Qu. Max. \n", "-0.4439993 -0.0783511 0.0047374 0.0789669 0.6795281 \n", "\n", "Coefficients:\n", " Estimate Std. Error t-value Pr(>|t|) \n", "lawyes -2.8036e-02 1.7354e-02 -1.6155 0.1064826 \n", "log_prisoners -1.0038e-01 2.7939e-02 -3.5929 0.0003416 ***\n", "afam -7.1718e-03 1.0982e-02 -0.6530 0.5138790 \n", "male 7.7340e-02 1.1293e-02 6.8486 1.242e-11 ***\n", "log_population 4.5431e-01 1.3025e+00 0.3488 0.7273123 \n", "income 2.7423e-06 6.1901e-06 0.4430 0.6578392 \n", "log_density -6.8362e-01 1.3150e+00 -0.5199 0.6032725 \n", "year1978 6.6651e-02 2.7825e-02 2.3953 0.0167726 * \n", "year1979 1.8490e-01 2.8192e-02 6.5587 8.358e-11 ***\n", "year1980 2.4706e-01 2.8463e-02 8.6800 < 2.2e-16 ***\n", "year1981 2.5483e-01 2.9091e-02 8.7598 < 2.2e-16 ***\n", "year1982 2.4767e-01 3.0731e-02 8.0594 1.996e-15 ***\n", "year1983 2.2548e-01 3.3088e-02 6.8145 1.560e-11 ***\n", "year1984 2.6672e-01 3.5930e-02 7.4233 2.292e-13 ***\n", "year1985 3.2463e-01 3.8814e-02 8.3637 < 2.2e-16 ***\n", "year1986 4.1205e-01 4.2406e-02 9.7168 < 2.2e-16 ***\n", "year1987 4.2034e-01 4.5912e-02 9.1552 < 2.2e-16 ***\n", "year1988 4.9126e-01 4.9628e-02 9.8990 < 2.2e-16 ***\n", "year1989 5.5570e-01 5.3167e-02 10.4520 < 2.2e-16 ***\n", "year1990 6.9005e-01 5.6364e-02 12.2428 < 2.2e-16 ***\n", "year1991 7.5413e-01 5.9185e-02 12.7419 < 2.2e-16 ***\n", "year1992 7.9616e-01 6.2477e-02 12.7432 < 2.2e-16 ***\n", "year1993 8.2778e-01 6.4733e-02 12.7877 < 2.2e-16 ***\n", "year1994 8.2324e-01 6.7360e-02 12.2214 < 2.2e-16 ***\n", "year1995 8.2840e-01 7.0212e-02 11.7986 < 2.2e-16 ***\n", "year1996 7.8340e-01 7.3044e-02 10.7250 < 2.2e-16 ***\n", "year1997 7.7190e-01 7.5635e-02 10.2056 < 2.2e-16 ***\n", "year1998 7.2570e-01 7.8486e-02 9.2463 < 2.2e-16 ***\n", "year1999 6.7540e-01 8.0617e-02 8.3779 < 2.2e-16 ***\n", "---\n", "Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n", "\n", "Total Sum of Squares: 36.789\n", "Residual Sum of Squares: 21.143\n", "R-Squared: 0.4253\n", "Adj. R-Squared: 0.38376\n", "F-statistic: 27.8915 on 29 and 1093 DF, p-value: < 2.22e-16" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Fixed Effects model\n", "\n", "fe_initial <- plm(\n", " formula_initial,\n", " data = guns,\n", " index = c(\"state\", \"year\"),\n", " model = \"within\"\n", ")\n", "\n", "summary(fe_initial)" ] }, { "cell_type": "code", "execution_count": 49, "id": "5a30085b-a5ae-4a82-a283-fe1fd4ec6da9", "metadata": { "vscode": { "languageId": "r" } }, "outputs": [ { "data": { "text/plain": [ "Oneway (individual) effect Random Effect Model \n", " (Swamy-Arora's transformation)\n", "\n", "Call:\n", "plm(formula = formula_initial, data = guns, model = \"random\", \n", " index = c(\"state\", \"year\"))\n", "\n", "Balanced Panel: n = 51, T = 23, N = 1173\n", "\n", "Effects:\n", " var std.dev share\n", "idiosyncratic 0.01934 0.13908 0.195\n", "individual 0.08006 0.28295 0.805\n", "theta: 0.898\n", "\n", "Residuals:\n", " Min. 1st Qu. Median 3rd Qu. Max. \n", "-0.5272917 -0.0868476 0.0066143 0.0914545 0.6896996 \n", "\n", "Coefficients:\n", " Estimate Std. Error z-value Pr(>|z|) \n", "(Intercept) 4.1693e+00 2.8042e-01 14.8682 < 2.2e-16 ***\n", "lawyes -3.3897e-02 1.8156e-02 -1.8670 0.061901 . \n", "log_prisoners 1.1240e-02 2.7985e-02 0.4017 0.687941 \n", "afam 2.4356e-02 7.6116e-03 3.1999 0.001375 ** \n", "male 7.5992e-02 1.1651e-02 6.5224 6.918e-11 ***\n", "log_population 1.1248e-01 4.2553e-02 2.6433 0.008210 ** \n", "income 1.1084e-05 6.1940e-06 1.7895 0.073533 . \n", "log_density 6.1650e-02 3.2553e-02 1.8938 0.058247 . \n", "year1978 5.1505e-02 2.9676e-02 1.7356 0.082640 . \n", "year1979 1.5491e-01 2.9958e-02 5.1710 2.329e-07 ***\n", "year1980 2.0945e-01 3.0186e-02 6.9386 3.961e-12 ***\n", "year1981 2.0710e-01 3.0720e-02 6.7413 1.570e-11 ***\n", "year1982 1.8189e-01 3.2175e-02 5.6531 1.576e-08 ***\n", "year1983 1.4012e-01 3.4284e-02 4.0870 4.371e-05 ***\n", "year1984 1.6499e-01 3.6842e-02 4.4784 7.519e-06 ***\n", "year1985 2.1031e-01 3.9527e-02 5.3207 1.034e-07 ***\n", "year1986 2.8359e-01 4.2902e-02 6.6100 3.842e-11 ***\n", "year1987 2.7897e-01 4.6224e-02 6.0352 1.588e-09 ***\n", "year1988 3.3629e-01 4.9734e-02 6.7619 1.362e-11 ***\n", "year1989 3.8660e-01 5.3058e-02 7.2864 3.184e-13 ***\n", "year1990 5.0215e-01 5.6492e-02 8.8887 < 2.2e-16 ***\n", "year1991 5.5516e-01 5.9235e-02 9.3721 < 2.2e-16 ***\n", "year1992 5.8184e-01 6.2295e-02 9.3401 < 2.2e-16 ***\n", "year1993 6.0154e-01 6.4392e-02 9.3418 < 2.2e-16 ***\n", "year1994 5.8386e-01 6.6826e-02 8.7370 < 2.2e-16 ***\n", "year1995 5.7472e-01 6.9467e-02 8.2733 < 2.2e-16 ***\n", "year1996 5.1602e-01 7.2071e-02 7.1599 8.071e-13 ***\n", "year1997 4.9087e-01 7.4396e-02 6.5981 4.165e-11 ***\n", "year1998 4.2789e-01 7.6883e-02 5.5656 2.613e-08 ***\n", "year1999 3.6428e-01 7.8725e-02 4.6272 3.706e-06 ***\n", "---\n", "Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n", "\n", "Total Sum of Squares: 41.486\n", "Residual Sum of Squares: 25.257\n", "R-Squared: 0.39119\n", "Adj. R-Squared: 0.37575\n", "Chisq: 734.448 on 29 DF, p-value: < 2.22e-16" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Random Effects model\n", "\n", "re_initial <- plm(\n", " formula_initial,\n", " data = guns,\n", " index = c(\"state\", \"year\"),\n", " model = \"random\"\n", ")\n", "\n", "summary(re_initial)" ] }, { "cell_type": "markdown", "id": "a53a50a9-ced9-4072-8cf9-d890b8727e97", "metadata": {}, "source": [ "## 8. Specification Refinement Before Hausman\n", "
\n", "\n", "תוצאות המודלים הראשוניים הראו\n", "Standard Errors\n", "גדולים במיוחד עבור\n", "log_population\n", "ו-log_density\n", "במודל\n", "Fixed Effects.\n", "\n", "מאחר שאמידת\n", "FE\n", "מבוססת על השינויים בתוך כל מדינה לאורך זמן, נבדוק האם שני המשתנים כמעט נעים יחד בתוך אותה מדינה.\n", "\n", "מטרת שלב זה אינה לסנן משתנים לפי מובהקות, אלא לוודא שהמפרט המשותף שישמש להשוואת\n", "FE\n", "ו-RE\n", "אינו סובל מבעיית\n", "multicollinearity\n", ".\n", "\n", "
" ] }, { "cell_type": "code", "execution_count": 52, "id": "7c4a35a5-8090-4428-864b-265c97a65a12", "metadata": { "vscode": { "languageId": "r" } }, "outputs": [ { "data": { "text/html": [ "0.999197995549733" ], "text/latex": [ "0.999197995549733" ], "text/markdown": [ "0.999197995549733" ], "text/plain": [ "[1] 0.999198" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Check within-state correlation between population and density\n", "\n", "log_population_within <- guns$log_population -\n", " ave(guns$log_population, guns$state)\n", "\n", "log_density_within <- guns$log_density -\n", " ave(guns$log_density, guns$state)\n", "\n", "cor(log_population_within, log_density_within)" ] }, { "cell_type": "markdown", "id": "ad116874-1ab6-471b-b97e-23b233487f11", "metadata": {}, "source": [ "
\n", "\n", "המתאם בין השינויים בתוך המדינה של\n", "log_population\n", "ושל\n", "log_density\n", "עומד על\n", "0.9992,\n", "ומצביע על כך ששני המשתנים מכילים כמעט אותו מידע מבחינת השונות לאורך זמן.\n", "\n", " שטחה של כל מדינה כמעט קבוע לאורך תקופת המדגם. לכן, בתוך אותה מדינה, שינוי בצפיפות משקף כמעט באופן מלא שינוי בגודל האוכלוסייה.\n", "\n", "מאחר שמודל\n", "Fixed Effects\n", "מזהה את המקדמים מתוך השינויים בתוך כל מדינה לאורך זמן, הכללת שני המשתנים יחד יוצרת\n", "multicollinearity\n", "כמעט מושלמת. תוצאה זו מסבירה את ה-\n", "Standard Errors\n", "הגדולים שהתקבלו עבורם באמידה הראשונית.\n", "\n", "לפיכך, נסיר את\n", "log_density\n", "ונשאיר את\n", "log_population.\n", "בחירה זו מונעת כפילות מידע ומאפשרת לשמור במודל מדד ישיר וברור לגודל האוכלוסייה של המדינה.\n", "\n", "לאחר הסרת\n", "log_density\n", "ניתן לאמוד מחדש את מודלי\n", "Fixed Effects\n", "ו-Random Effects\n", "על בסיס מפרט משותף ויציב יותר, ולאחר מכן להשוות ביניהם באמצעות מבחן\n", "Hausman.\n", "\n", "
" ] }, { "cell_type": "code", "execution_count": 55, "id": "1ce4778f-37a5-494b-8c85-77cea99cc245", "metadata": { "vscode": { "languageId": "r" } }, "outputs": [], "source": [ "# Reduced model specification after removing within multicollinearity\n", "\n", "formula_reduced <- log_violent ~\n", " law +\n", " log_prisoners +\n", " afam +\n", " male +\n", " log_population +\n", " income +\n", " year" ] }, { "cell_type": "code", "execution_count": 57, "id": "0826a349-284c-4422-8b48-621712199287", "metadata": { "vscode": { "languageId": "r" } }, "outputs": [ { "data": { "text/plain": [ "Oneway (individual) effect Within Model\n", "\n", "Call:\n", "plm(formula = formula_reduced, data = guns, model = \"within\", \n", " index = c(\"state\", \"year\"))\n", "\n", "Balanced Panel: n = 51, T = 23, N = 1173\n", "\n", "Residuals:\n", " Min. 1st Qu. Median 3rd Qu. Max. \n", "-0.4438817 -0.0783732 0.0047202 0.0789621 0.6804231 \n", "\n", "Coefficients:\n", " Estimate Std. Error t-value Pr(>|t|) \n", "lawyes -2.9202e-02 1.7202e-02 -1.6976 0.0898723 . \n", "log_prisoners -1.0194e-01 2.7768e-02 -3.6709 0.0002534 ***\n", "afam -7.4590e-03 1.0965e-02 -0.6803 0.4964824 \n", "male 7.8448e-02 1.1086e-02 7.0764 2.639e-12 ***\n", "log_population -2.2189e-01 6.7885e-02 -3.2686 0.0011144 ** \n", "income 2.0050e-06 6.0234e-06 0.3329 0.7392983 \n", "year1978 6.7160e-02 2.7799e-02 2.4159 0.0158577 * \n", "year1979 1.8557e-01 2.8153e-02 6.5915 6.756e-11 ***\n", "year1980 2.4720e-01 2.8452e-02 8.6883 < 2.2e-16 ***\n", "year1981 2.5519e-01 2.9073e-02 8.7776 < 2.2e-16 ***\n", "year1982 2.4840e-01 3.0688e-02 8.0943 1.523e-15 ***\n", "year1983 2.2680e-01 3.2978e-02 6.8775 1.023e-11 ***\n", "year1984 2.6889e-01 3.5674e-02 7.5374 1.003e-13 ***\n", "year1985 3.2741e-01 3.8430e-02 8.5198 < 2.2e-16 ***\n", "year1986 4.1553e-01 4.1857e-02 9.9274 < 2.2e-16 ***\n", "year1987 4.2444e-01 4.5214e-02 9.3873 < 2.2e-16 ***\n", "year1988 4.9600e-01 4.8766e-02 10.1711 < 2.2e-16 ***\n", "year1989 5.6102e-01 5.2156e-02 10.7565 < 2.2e-16 ***\n", "year1990 6.9441e-01 5.5717e-02 12.4633 < 2.2e-16 ***\n", "year1991 7.5874e-01 5.8496e-02 12.9707 < 2.2e-16 ***\n", "year1992 8.0128e-01 6.1677e-02 12.9915 < 2.2e-16 ***\n", "year1993 8.3312e-01 6.3890e-02 13.0401 < 2.2e-16 ***\n", "year1994 8.2895e-01 6.6436e-02 12.4774 < 2.2e-16 ***\n", "year1995 8.3451e-01 6.9201e-02 12.0592 < 2.2e-16 ***\n", "year1996 7.8993e-01 7.1933e-02 10.9815 < 2.2e-16 ***\n", "year1997 7.7886e-01 7.4417e-02 10.4662 < 2.2e-16 ***\n", "year1998 7.3320e-01 7.7126e-02 9.5064 < 2.2e-16 ***\n", "year1999 6.8322e-01 7.9173e-02 8.6295 < 2.2e-16 ***\n", "---\n", "Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n", "\n", "Total Sum of Squares: 36.789\n", "Residual Sum of Squares: 21.148\n", "R-Squared: 0.42516\n", "Adj. R-Squared: 0.38417\n", "F-statistic: 28.8973 on 28 and 1094 DF, p-value: < 2.22e-16" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Fixed Effects reduced model\n", "\n", "fe_reduced <- plm(\n", " formula_reduced,\n", " data = guns,\n", " index = c(\"state\", \"year\"),\n", " model = \"within\"\n", ")\n", "\n", "summary(fe_reduced)" ] }, { "cell_type": "code", "execution_count": 59, "id": "512942c7-5b4a-4229-a9c4-cf33cc215c28", "metadata": { "vscode": { "languageId": "r" } }, "outputs": [ { "data": { "text/plain": [ "Oneway (individual) effect Random Effect Model \n", " (Swamy-Arora's transformation)\n", "\n", "Call:\n", "plm(formula = formula_reduced, data = guns, model = \"random\", \n", " index = c(\"state\", \"year\"))\n", "\n", "Balanced Panel: n = 51, T = 23, N = 1173\n", "\n", "Effects:\n", " var std.dev share\n", "idiosyncratic 0.01933 0.13904 0.197\n", "individual 0.07865 0.28045 0.803\n", "theta: 0.8972\n", "\n", "Residuals:\n", " Min. 1st Qu. Median 3rd Qu. Max. \n", "-0.5189354 -0.0840227 0.0078915 0.0929493 0.6957402 \n", "\n", "Coefficients:\n", " Estimate Std. Error z-value Pr(>|z|) \n", "(Intercept) 3.9799e+00 2.6381e-01 15.0864 < 2.2e-16 ***\n", "lawyes -3.1401e-02 1.8144e-02 -1.7307 0.08351 . \n", "log_prisoners 1.1883e-02 2.8023e-02 0.4240 0.67154 \n", "afam 3.0035e-02 7.0276e-03 4.2739 1.921e-05 ***\n", "male 7.2407e-02 1.1523e-02 6.2837 3.305e-10 ***\n", "log_population 1.5705e-01 3.5848e-02 4.3811 1.181e-05 ***\n", "income 1.2652e-05 6.1540e-06 2.0559 0.03979 * \n", "year1978 5.0102e-02 2.9731e-02 1.6852 0.09195 . \n", "year1979 1.5293e-01 3.0006e-02 5.0967 3.457e-07 ***\n", "year1980 2.0727e-01 3.0232e-02 6.8561 7.077e-12 ***\n", "year1981 2.0426e-01 3.0755e-02 6.6414 3.106e-11 ***\n", "year1982 1.7803e-01 3.2190e-02 5.5306 3.191e-08 ***\n", "year1983 1.3476e-01 3.4262e-02 3.9333 8.380e-05 ***\n", "year1984 1.5742e-01 3.6740e-02 4.2848 1.829e-05 ***\n", "year1985 2.0100e-01 3.9354e-02 5.1075 3.265e-07 ***\n", "year1986 2.7236e-01 4.2647e-02 6.3864 1.699e-10 ***\n", "year1987 2.6598e-01 4.5889e-02 5.7961 6.786e-09 ***\n", "year1988 3.2145e-01 4.9310e-02 6.5189 7.084e-11 ***\n", "year1989 3.7008e-01 5.2555e-02 7.0417 1.899e-12 ***\n", "year1990 4.8435e-01 5.5944e-02 8.6577 < 2.2e-16 ***\n", "year1991 5.3646e-01 5.8657e-02 9.1456 < 2.2e-16 ***\n", "year1992 5.6169e-01 6.1650e-02 9.1110 < 2.2e-16 ***\n", "year1993 5.8056e-01 6.3715e-02 9.1119 < 2.2e-16 ***\n", "year1994 5.6182e-01 6.6102e-02 8.4992 < 2.2e-16 ***\n", "year1995 5.5165e-01 6.8703e-02 8.0294 9.793e-16 ***\n", "year1996 4.9182e-01 7.1258e-02 6.9019 5.131e-12 ***\n", "year1997 4.6551e-01 7.3527e-02 6.3312 2.433e-10 ***\n", "year1998 4.0120e-01 7.5946e-02 5.2827 1.273e-07 ***\n", "year1999 3.3662e-01 7.7740e-02 4.3300 1.491e-05 ***\n", "---\n", "Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n", "\n", "Total Sum of Squares: 41.566\n", "Residual Sum of Squares: 25.386\n", "R-Squared: 0.38926\n", "Adj. R-Squared: 0.37431\n", "Chisq: 729.144 on 28 DF, p-value: < 2.22e-16" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Random Effects reduced model\n", "\n", "re_reduced <- plm(\n", " formula_reduced,\n", " data = guns,\n", " index = c(\"state\", \"year\"),\n", " model = \"random\"\n", ")\n", "\n", "summary(re_reduced)" ] }, { "cell_type": "markdown", "id": "37a81d3b-3d69-4d4f-8c88-d00331c8269d", "metadata": {}, "source": [ "
\n", "\n", "לאחר הסרת\n", "log_density\n", "הרצנו מחדש את מודלי\n", "Fixed Effects\n", "ו-Random Effects\n", "על אותו מפרט מצומצם.\n", "\n", "ה-\n", "Standard Errors\n", "החריגים שנצפו קודם עבור משתני האוכלוסייה והצפיפות נעלמו, ולכן בעיית ה-\n", "multicollinearity\n", "טופלה.\n", "\n", "מפרט משותף זה ישמש כעת לביצוע מבחן\n", "Hausman.\n", "בשלב זה איננו מבצעים עדיין סינון לפי מובהקות. סינון כזה יתבצע לאחר בחירת המודל.\n", "\n", "
" ] }, { "cell_type": "markdown", "id": "b2bbfa32-c953-4012-a472-ccd205d07e1b", "metadata": {}, "source": [ "### Reduced Model Equation\n", "\n", "
\n", "\n", "לאחר הסרת\n", "log_density\n", "עקב ה-\n", "multicollinearity\n", "החזקה עם\n", "log_population\n", "בתוך המדינות, המשוואה ששימשה להשוואת מודלי\n", "FE\n", "ו-RE\n", "היא:\n", "\n", "
\n", "\n", "$$\n", "\\ln(violent_{it}) =\n", "\\alpha\n", "+ \\beta_1 law_{it}\n", "+ \\beta_2 \\ln(prisoners_{it})\n", "+ \\beta_3 afam_{it}\n", "+ \\beta_4 male_{it}\n", "+ \\beta_5 \\ln(population_{it})\n", "+ \\beta_6 income_{it}\n", "+ \\sum_{t=1978}^{1999}\\gamma_t D_t\n", "+ u_{it}\n", "$$" ] }, { "cell_type": "markdown", "id": "808d36f1-9493-447a-815b-c1d8b97566a3", "metadata": {}, "source": [ "## 9. Hausman Test and Model Selection\n", "\n", "
\n", "\n", "לאחר קביעת מפרט משותף וסופי לשני המודלים, נשתמש במבחן\n", "Hausman\n", "כדי לבחור בין\n", "Fixed Effects\n", "ל-Random Effects.\n", "\n", "השערת האפס היא שמודל\n", "Random Effects\n", "מתאים, כלומר האפקטים הייחודיים של המדינות אינם מתואמים עם המשתנים המסבירים.\n", "\n", "אם ערך ה-\n", "p-value\n", "קטן מ-0.05, נדחה את השערת האפס ונעדיף את מודל\n", "Fixed Effects.\n", "אחרת, נעדיף את מודל\n", "Random Effects.\n", "\n", "
" ] }, { "cell_type": "code", "execution_count": 64, "id": "24a214e1-eecd-4967-85b0-3d48581e69f3", "metadata": { "vscode": { "languageId": "r" } }, "outputs": [ { "data": { "text/plain": [ "\n", "\tHausman Test\n", "\n", "data: formula_reduced\n", "chisq = 38.504, df = 28, p-value = 0.08924\n", "alternative hypothesis: one model is inconsistent\n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Hausman test\n", "\n", "hausman_test <- phtest(fe_reduced, re_reduced)\n", "\n", "hausman_test" ] }, { "cell_type": "markdown", "id": "b1d6ee03-2f81-4398-841a-b1c7cd666695", "metadata": {}, "source": [ "
\n", "\n", "במבחן\n", "Hausman\n", "התקבל ערך\n", "p-value = 0.0892.\n", "\n", "מכיוון שערך זה גדול מרמת המובהקות של 5%, איננו דוחים את השערת האפס של המבחן.\n", "\n", "לכן אין עדות מספקת לכך שהאפקטים הייחודיים של המדינות מתואמים עם המשתנים המסבירים, ובהתאם נבחר במודל\n", "Random Effects\n", "כמודל המתאים להמשך הניתוח.\n", "\n", "מכאן והלאה בדיקות השאריות ותיקוני המודל, במידת הצורך, יבוצעו על מודל\n", "Random Effects\n", "שנבחר.\n", "\n", "
" ] }, { "cell_type": "markdown", "id": "e9ad70d9-00fa-4102-8dc1-175b6daa1000", "metadata": {}, "source": [ "## 10. Variable Selection in the Selected Model\n", "\n", "
\n", "\n", "לאחר שמבחן\n", "Hausman\n", "הוביל לבחירת מודל\n", "Random Effects,\n", "בחנו את מובהקות המשתנים המסבירים במודל הנבחר.\n", "\n", "המשתנה\n", "log_prisoners\n", "לא נמצא מובהק, עם\n", "p-value = 0.672,\n", "ולכן הוסר מהמפרט.\n", "\n", "המשתנים\n", "afam,\n", "male,\n", "log_population\n", "ו-income\n", "נמצאו מובהקים ברמת 5%.\n", "\n", "המשתנה\n", "law\n", "התקבל עם\n", "p-value = 0.084.\n", "מושאר במכוון במפרט למרות מובהקות גבולית, משום שהוא מהווה את מוקד שאלת המחקר המרכזית, ובלעדיו המודל מאבד את משמעותו.\n", "\n", "השארת המשתנה מאפשרת לבחון באופן ישיר האם קיומו של חוק\n", "Shall-Carry\n", "קשור לשיעור הפשיעה האלימה, גם אם בסופו של דבר ההשפעה אינה מובהקת ברמת 5%.\n", "\n", "משתני השנה נשארים במודל כמשתני בקרה להשפעות משותפות לכל המדינות לאורך זמן.\n", "\n", "הסינון יתבצע באופן הדרגתי: בכל שלב יוסר המסביר שאינו מובהק ובעל ערך ה-\n", "p-value\n", "הגבוה ביותר, ולאחר מכן המודל ייאמד מחדש.\n", "
" ] }, { "cell_type": "code", "execution_count": 68, "id": "32fc7c84-852f-4466-9c81-25d8a6205031", "metadata": { "vscode": { "languageId": "r" } }, "outputs": [ { "data": { "text/plain": [ "Oneway (individual) effect Random Effect Model \n", " (Swamy-Arora's transformation)\n", "\n", "Call:\n", "plm(formula = formula_step1, data = guns, model = \"random\", index = c(\"state\", \n", " \"year\"))\n", "\n", "Balanced Panel: n = 51, T = 23, N = 1173\n", "\n", "Effects:\n", " var std.dev share\n", "idiosyncratic 0.01955 0.13983 0.092\n", "individual 0.19363 0.44004 0.908\n", "theta: 0.9339\n", "\n", "Residuals:\n", " Min. 1st Qu. Median 3rd Qu. Max. \n", "-0.5096851 -0.0795459 0.0083383 0.0914193 0.6825377 \n", "\n", "Coefficients:\n", " Estimate Std. Error z-value Pr(>|z|) \n", "(Intercept) 4.1764e+00 2.3018e-01 18.1441 < 2.2e-16 ***\n", "lawyes -2.9182e-02 1.7429e-02 -1.6743 0.09407 . \n", "afam 1.5850e-02 8.4788e-03 1.8693 0.06158 . \n", "male 7.6384e-02 1.1219e-02 6.8082 9.882e-12 ***\n", "log_population 6.1688e-02 4.5961e-02 1.3422 0.17954 \n", "income 7.9234e-06 6.0593e-06 1.3076 0.19100 \n", "year1978 5.5364e-02 2.8562e-02 1.9384 0.05258 . \n", "year1979 1.6138e-01 2.8729e-02 5.6171 1.942e-08 ***\n", "year1980 2.1715e-01 2.8902e-02 7.5135 5.757e-14 ***\n", "year1981 2.1692e-01 2.9319e-02 7.3985 1.378e-13 ***\n", "year1982 1.9436e-01 3.0203e-02 6.4353 1.232e-10 ***\n", "year1983 1.5604e-01 3.1579e-02 4.9412 7.765e-07 ***\n", "year1984 1.8490e-01 3.3848e-02 5.4629 4.685e-08 ***\n", "year1985 2.3302e-01 3.6258e-02 6.4267 1.304e-10 ***\n", "year1986 3.0910e-01 3.9195e-02 7.8862 3.114e-15 ***\n", "year1987 3.0704e-01 4.2125e-02 7.2888 3.128e-13 ***\n", "year1988 3.6724e-01 4.5294e-02 8.1079 5.150e-16 ***\n", "year1989 4.2055e-01 4.8250e-02 8.7161 < 2.2e-16 ***\n", "year1990 5.3884e-01 5.0790e-02 10.6090 < 2.2e-16 ***\n", "year1991 5.9342e-01 5.2998e-02 11.1972 < 2.2e-16 ***\n", "year1992 6.2341e-01 5.5672e-02 11.1978 < 2.2e-16 ***\n", "year1993 6.4557e-01 5.7445e-02 11.2380 < 2.2e-16 ***\n", "year1994 6.3082e-01 5.9578e-02 10.5882 < 2.2e-16 ***\n", "year1995 6.2420e-01 6.1568e-02 10.1383 < 2.2e-16 ***\n", "year1996 5.6801e-01 6.3598e-02 8.9312 < 2.2e-16 ***\n", "year1997 5.4577e-01 6.5510e-02 8.3311 < 2.2e-16 ***\n", "year1998 4.8676e-01 6.7572e-02 7.2037 5.862e-13 ***\n", "year1999 4.2619e-01 6.9064e-02 6.1709 6.791e-10 ***\n", "---\n", "Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n", "\n", "Total Sum of Squares: 38.764\n", "Residual Sum of Squares: 23.438\n", "R-Squared: 0.39535\n", "Adj. R-Squared: 0.38109\n", "Chisq: 748.665 on 27 DF, p-value: < 2.22e-16" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Random Effects model after removing log_prisoners\n", "\n", "formula_step1 <- log_violent ~\n", " law +\n", " afam +\n", " male +\n", " log_population +\n", " income +\n", " year\n", "\n", "re_step1 <- plm(\n", " formula_step1,\n", " data = guns,\n", " index = c(\"state\", \"year\"),\n", " model = \"random\"\n", ")\n", "\n", "summary(re_step1)" ] }, { "cell_type": "markdown", "id": "d80ffa20-9cd2-4dd1-9db9-e35361a506d5", "metadata": {}, "source": [ "
\n", "\n", "במודל המעודכן,\n", "income\n", "הוא המשתנה המסביר בעל ערך ה-\n", "p-value\n", "הגבוה ביותר\n", "(0.191).\n", "\n", "לכן, במסגרת תהליך סינון המשתנים, נסיר בשלב הבא את\n", "income\n", "ונאמוד את המודל מחדש.\n", "\n", "
" ] }, { "cell_type": "code", "execution_count": 71, "id": "9ae7bd31-2195-4efb-8441-763588ce4a22", "metadata": { "vscode": { "languageId": "r" } }, "outputs": [ { "data": { "text/plain": [ "Oneway (individual) effect Random Effect Model \n", " (Swamy-Arora's transformation)\n", "\n", "Call:\n", "plm(formula = formula_step2, data = guns, model = \"random\", index = c(\"state\", \n", " \"year\"))\n", "\n", "Balanced Panel: n = 51, T = 23, N = 1173\n", "\n", "Effects:\n", " var std.dev share\n", "idiosyncratic 0.01953 0.13976 0.089\n", "individual 0.19935 0.44648 0.911\n", "theta: 0.9349\n", "\n", "Residuals:\n", " Min. 1st Qu. Median 3rd Qu. Max. \n", "-0.5096125 -0.0787621 0.0085484 0.0907753 0.6731014 \n", "\n", "Coefficients:\n", " Estimate Std. Error z-value Pr(>|z|) \n", "(Intercept) 4.2593505 0.2223480 19.1562 < 2.2e-16 ***\n", "lawyes -0.0334290 0.0170894 -1.9561 0.05045 . \n", "afam 0.0154222 0.0085261 1.8088 0.07048 . \n", "male 0.0774355 0.0111911 6.9194 4.536e-12 ***\n", "log_population 0.0553699 0.0462543 1.1971 0.23128 \n", "year1978 0.0594290 0.0283792 2.0941 0.03625 * \n", "year1979 0.1652466 0.0285694 5.7841 7.292e-09 ***\n", "year1980 0.2182705 0.0288755 7.5590 4.061e-14 ***\n", "year1981 0.2188757 0.0292742 7.4767 7.619e-14 ***\n", "year1982 0.1962709 0.0301627 6.5071 7.663e-11 ***\n", "year1983 0.1601041 0.0314426 5.0919 3.544e-07 ***\n", "year1984 0.1943250 0.0331445 5.8630 4.547e-09 ***\n", "year1985 0.2453103 0.0351273 6.9835 2.880e-12 ***\n", "year1986 0.3245277 0.0375227 8.6488 < 2.2e-16 ***\n", "year1987 0.3248655 0.0400348 8.1146 4.875e-16 ***\n", "year1988 0.3880270 0.0426308 9.1020 < 2.2e-16 ***\n", "year1989 0.4440386 0.0450403 9.8587 < 2.2e-16 ***\n", "year1990 0.5632244 0.0475168 11.8532 < 2.2e-16 ***\n", "year1991 0.6171401 0.0500683 12.3260 < 2.2e-16 ***\n", "year1992 0.6500455 0.0521302 12.4696 < 2.2e-16 ***\n", "year1993 0.6728963 0.0538485 12.4961 < 2.2e-16 ***\n", "year1994 0.6603045 0.0555254 11.8919 < 2.2e-16 ***\n", "year1995 0.6555802 0.0571090 11.4795 < 2.2e-16 ***\n", "year1996 0.6019005 0.0585278 10.2840 < 2.2e-16 ***\n", "year1997 0.5829255 0.0595357 9.7912 < 2.2e-16 ***\n", "year1998 0.5287042 0.0600695 8.8015 < 2.2e-16 ***\n", "year1999 0.4709197 0.0606547 7.7639 8.233e-15 ***\n", "---\n", "Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n", "\n", "Total Sum of Squares: 38.706\n", "Residual Sum of Squares: 23.426\n", "R-Squared: 0.39478\n", "Adj. R-Squared: 0.38105\n", "Chisq: 747.528 on 26 DF, p-value: < 2.22e-16" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Random Effects model after removing income\n", "\n", "formula_step2 <- log_violent ~\n", " law +\n", " afam +\n", " male +\n", " log_population +\n", " year\n", "\n", "re_step2 <- plm(\n", " formula_step2,\n", " data = guns,\n", " index = c(\"state\", \"year\"),\n", " model = \"random\"\n", ")\n", "\n", "summary(re_step2)" ] }, { "cell_type": "markdown", "id": "6bf7fdec-c6fd-4e6c-ae03-7b69e9bb923b", "metadata": {}, "source": [ "
\n", "\n", "במודל המעודכן,\n", "log_population\n", "הוא המשתנה המסביר בעל ערך ה-\n", "p-value\n", "הגבוה ביותר\n", "(0.231),\n", "ולכן אינו מובהק ברמת 5%.\n", "\n", "לעומתו,\n", "law\n", "נמצא קרוב מאוד לרמת מובהקות של 5%,\n", "afam\n", "מציג מובהקות חלשה ברמת 10%,\n", "ו-male\n", "מובהק מאוד.\n", "\n", "לכן נסיר בשלב זה רק את\n", "log_population\n", "ונאמוד מחדש את המודל לפני קבלת החלטה נוספת.\n", "\n", "
" ] }, { "cell_type": "code", "execution_count": 74, "id": "91c4eec9-b515-46bc-b9e6-02a1cce0e3a1", "metadata": { "vscode": { "languageId": "r" } }, "outputs": [ { "data": { "text/plain": [ "Oneway (individual) effect Random Effect Model \n", " (Swamy-Arora's transformation)\n", "\n", "Call:\n", "plm(formula = formula_step3, data = guns, model = \"random\", index = c(\"state\", \n", " \"year\"))\n", "\n", "Balanced Panel: n = 51, T = 23, N = 1173\n", "\n", "Effects:\n", " var std.dev share\n", "idiosyncratic 0.01966 0.14020 0.073\n", "individual 0.24807 0.49806 0.927\n", "theta: 0.9414\n", "\n", "Residuals:\n", " Min. 1st Qu. Median 3rd Qu. Max. \n", "-0.5097268 -0.0782339 0.0091033 0.0893284 0.6665329 \n", "\n", "Coefficients:\n", " Estimate Std. Error z-value Pr(>|z|) \n", "(Intercept) 4.3247267 0.2159838 20.0234 < 2.2e-16 ***\n", "lawyes -0.0312279 0.0169162 -1.8460 0.06489 . \n", "afam 0.0131246 0.0087222 1.5047 0.13239 \n", "male 0.0773923 0.0110933 6.9765 3.026e-12 ***\n", "year1978 0.0602469 0.0281798 2.1379 0.03252 * \n", "year1979 0.1668951 0.0283629 5.8843 3.998e-09 ***\n", "year1980 0.2207767 0.0286626 7.7026 1.333e-14 ***\n", "year1981 0.2220089 0.0290500 7.6423 2.134e-14 ***\n", "year1982 0.2000331 0.0299339 6.6825 2.349e-11 ***\n", "year1983 0.1644677 0.0312096 5.2698 1.366e-07 ***\n", "year1984 0.1992319 0.0329106 6.0537 1.415e-09 ***\n", "year1985 0.2506967 0.0348942 7.1845 6.746e-13 ***\n", "year1986 0.3302831 0.0372930 8.8564 < 2.2e-16 ***\n", "year1987 0.3310094 0.0398078 8.3152 < 2.2e-16 ***\n", "year1988 0.3946228 0.0424040 9.3063 < 2.2e-16 ***\n", "year1989 0.4511548 0.0448120 10.0677 < 2.2e-16 ***\n", "year1990 0.5708145 0.0472889 12.0708 < 2.2e-16 ***\n", "year1991 0.6252803 0.0498337 12.5473 < 2.2e-16 ***\n", "year1992 0.6588714 0.0518889 12.6977 < 2.2e-16 ***\n", "year1993 0.6824688 0.0535971 12.7333 < 2.2e-16 ***\n", "year1994 0.6705691 0.0552627 12.1342 < 2.2e-16 ***\n", "year1995 0.6663261 0.0568400 11.7228 < 2.2e-16 ***\n", "year1996 0.6130514 0.0582565 10.5233 < 2.2e-16 ***\n", "year1997 0.5945494 0.0592617 10.0326 < 2.2e-16 ***\n", "year1998 0.5408986 0.0597925 9.0463 < 2.2e-16 ***\n", "year1999 0.4836876 0.0603751 8.0114 1.134e-15 ***\n", "---\n", "Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n", "\n", "Total Sum of Squares: 38.34\n", "Residual Sum of Squares: 23.121\n", "R-Squared: 0.39696\n", "Adj. R-Squared: 0.38381\n", "Chisq: 755.025 on 25 DF, p-value: < 2.22e-16" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Random Effects model after removing log_population\n", "\n", "formula_step3 <- log_violent ~\n", " law +\n", " afam +\n", " male +\n", " year\n", "\n", "re_step3 <- plm(\n", " formula_step3,\n", " data = guns,\n", " index = c(\"state\", \"year\"),\n", " model = \"random\"\n", ")\n", "\n", "summary(re_step3)" ] }, { "cell_type": "markdown", "id": "db3fd26e-6dba-4975-ad97-ceeeaeadafcf", "metadata": {}, "source": [ "
\n", "\n", "המשתנה\n", "afam\n", "נותר לא מובהק, עם\n", "p-value = 0.132,\n", "ולכן יוסר מהמפרט.\n", "\n", "המשתנה\n", "male\n", "נמצא מובהק מאוד, ואילו\n", "law\n", "מציג מובהקות חלשה ברמת 10% ונשאר במודל בשל תפקידו כמשתנה המדיניות המרכזי של הניתוח.\n", "\n", "
" ] }, { "cell_type": "code", "execution_count": 77, "id": "6aad28d1-be91-44e7-8da6-17494fb6b239", "metadata": { "vscode": { "languageId": "r" } }, "outputs": [ { "data": { "text/plain": [ "Oneway (individual) effect Random Effect Model \n", " (Swamy-Arora's transformation)\n", "\n", "Call:\n", "plm(formula = formula_final, data = guns, model = \"random\", index = c(\"state\", \n", " \"year\"))\n", "\n", "Balanced Panel: n = 51, T = 23, N = 1173\n", "\n", "Effects:\n", " var std.dev share\n", "idiosyncratic 0.01967 0.14024 0.061\n", "individual 0.30480 0.55208 0.939\n", "theta: 0.9471\n", "\n", "Residuals:\n", " Min. 1st Qu. Median 3rd Qu. Max. \n", "-0.5085534 -0.0755914 0.0095222 0.0886114 0.6611378 \n", "\n", "Coefficients:\n", " Estimate Std. Error z-value Pr(>|z|) \n", "(Intercept) 4.334922 0.217348 19.9446 < 2.2e-16 ***\n", "lawyes -0.032118 0.016791 -1.9128 0.05577 . \n", "male 0.080238 0.010908 7.3555 1.902e-13 ***\n", "year1978 0.061330 0.028009 2.1896 0.02855 * \n", "year1979 0.169082 0.028166 6.0031 1.936e-09 ***\n", "year1980 0.224541 0.028397 7.9073 2.630e-15 ***\n", "year1981 0.226542 0.028739 7.8826 3.206e-15 ***\n", "year1982 0.205911 0.029528 6.9734 3.094e-12 ***\n", "year1983 0.171634 0.030700 5.5906 2.262e-08 ***\n", "year1984 0.207784 0.032279 6.4371 1.218e-10 ***\n", "year1985 0.260635 0.034134 7.6357 2.246e-14 ***\n", "year1986 0.341700 0.036386 9.3911 < 2.2e-16 ***\n", "year1987 0.343970 0.038742 8.8786 < 2.2e-16 ***\n", "year1988 0.409172 0.041168 9.9391 < 2.2e-16 ***\n", "year1989 0.467230 0.043407 10.7639 < 2.2e-16 ***\n", "year1990 0.588551 0.045682 12.8837 < 2.2e-16 ***\n", "year1991 0.644396 0.048068 13.4058 < 2.2e-16 ***\n", "year1992 0.679366 0.049949 13.6011 < 2.2e-16 ***\n", "year1993 0.704120 0.051514 13.6685 < 2.2e-16 ***\n", "year1994 0.693267 0.053052 13.0676 < 2.2e-16 ***\n", "year1995 0.690072 0.054484 12.6656 < 2.2e-16 ***\n", "year1996 0.637885 0.055736 11.4448 < 2.2e-16 ***\n", "year1997 0.620397 0.056577 10.9656 < 2.2e-16 ***\n", "year1998 0.567713 0.056939 9.9705 < 2.2e-16 ***\n", "year1999 0.511512 0.057342 8.9203 < 2.2e-16 ***\n", "---\n", "Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n", "\n", "Total Sum of Squares: 38.053\n", "Residual Sum of Squares: 22.875\n", "R-Squared: 0.39885\n", "Adj. R-Squared: 0.38629\n", "Chisq: 761.684 on 24 DF, p-value: < 2.22e-16" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Final Random Effects model\n", "\n", "formula_final <- log_violent ~\n", " law +\n", " male +\n", " year\n", "\n", "re_final <- plm(\n", " formula_final,\n", " data = guns,\n", " index = c(\"state\", \"year\"),\n", " model = \"random\"\n", ")\n", "\n", "summary(re_final)" ] }, { "cell_type": "markdown", "id": "c5634a53-a3a5-4666-b2f9-2ee3e8571010", "metadata": {}, "source": [ "
\n", "\n", "לאחר תהליך סינון המשתנים התקבל המודל הסופי.\n", "\n", "המשתנה\n", "male\n", "נמצא מובהק מאוד\n", "(p-value < 0.001).\n", "\n", "המשתנה\n", "law\n", "התקבל עם\n", "p-value = 0.056.\n", "לכן הוא אינו מובהק ברמת 5%, אך מציג מובהקות חלשה ברמת 10%. המשתנה נשמר במודל בשל תפקידו כמשתנה המדיניות המרכזי של הניתוח.\n", "\n", "משתני השנה נמצאו ברובם המכריע מובהקים מאוד ונשמרו במודל כדי לשלוט בשינויים המשותפים לכל המדינות לאורך זמן.\n", "\n", "למודל הסופי התקבל\n", "R² = 0.399.\n", "\n", "מאחר שבשלב זה טרם נבדק מבנה השגיאה, המסקנות הסופיות לגבי מובהקות המקדמים ייקבעו לאחר ביצוע בדיקות השאריות והתיקון המתאים במידת הצורך.\n", "\n", "מודל זה ייחשב למודל\n", "Random Effects\n", "הסופי, ועליו נבצע את בדיקות השגיאה.\n", "\n", "
" ] }, { "cell_type": "markdown", "id": "66273912-9572-4f85-b00e-cdb33c52a8c4", "metadata": {}, "source": [ "### Final Model Equation\n", "\n", "
\n", "\n", "לאחר בחירת מודל\n", "Random Effects\n", "וסיום תהליך סינון המשתנים, המפרט הסופי הוא:\n", "\n", "
\n", "\n", "$$\n", "\\ln(violent_{it}) =\n", "\\alpha\n", "+ \\beta_1 law_{it}\n", "+ \\beta_2 male_{it}\n", "+ \\sum_{t=1978}^{1999}\\gamma_t D_t\n", "+ \\mu_i\n", "+ \\varepsilon_{it}\n", "$$\n", "\n", "
\n", "\n", "במשוואה הסופית:\n", "\n", "- $law_{it}$ מציין האם חוק Shall-Carry היה בתוקף במדינה ובשנה הנתונות.\n", "- $male_{it}$ הוא אחוז הגברים בגילאי 10–29.\n", "- $\\gamma_t$ מייצגים השפעות שנה ביחס לשנת הבסיס 1977.\n", "- $\\mu_i$ הוא האפקט האקראי הייחודי למדינה.\n", "- $\\varepsilon_{it}$ הוא רכיב השגיאה המשתנה בין מדינה ושנה.\n", "\n", "מודל זה הוא המודל שעליו יבוצעו בדיקות השאריות וה-\n", "misspecification.\n", "\n", "
" ] }, { "cell_type": "markdown", "id": "3bf78e3d-4d88-40c8-a659-afe496523108", "metadata": {}, "source": [ "## 11. Residual Diagnostics\n", "\n", "
\n", "\n", "לאחר קביעת מודל\n", "Random Effects\n", "הסופי, נבחן את שאריות המודל כדי לבדוק האם קיימות בעיות במבנה השגיאה.\n", "\n", "נבחן תחילה את פיזור השאריות ביחס לערכים החזויים. לאחר מכן נבדוק\n", "heteroskedasticity\n", "ואת נורמליות השאריות.\n", "\n", "
" ] }, { "cell_type": "code", "execution_count": 82, "id": "3c1c41bc-79c3-41af-a11b-b09a27b094a0", "metadata": { "vscode": { "languageId": "r" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "Plot with title \"Residuals vs Fitted - Final Random Effects Model\"" ] }, "metadata": { "image/png": { "height": 420, "width": 720 } }, "output_type": "display_data" } ], "source": [ "# Residuals vs Fitted - final Random Effects model\n", "\n", "res_final <- as.numeric(resid(re_final))\n", "fit_final <- as.numeric(fitted(re_final))\n", "\n", "options(repr.plot.width = 12, repr.plot.height = 7)\n", "\n", "plot(\n", " fit_final,\n", " res_final,\n", " main = \"Residuals vs Fitted - Final Random Effects Model\",\n", " xlab = \"Fitted Values\",\n", " ylab = \"Residuals\",\n", " pch = 20\n", ")\n", "\n", "abline(h = 0, col = \"red\")" ] }, { "cell_type": "markdown", "id": "35b6e1b4-b969-4e7e-955b-2b9bfaf9eae2", "metadata": {}, "source": [ "
\n", "\n", "גרף\n", "Residuals vs Fitted\n", "מראה כי השאריות מפוזרות באופן כללי סביב אפס, ללא מגמה או תבנית לא-ליניארית ברורה.\n", "\n", "עם זאת, מידת הפיזור של השאריות אינה נראית אחידה לחלוטין לאורך כל טווח הערכים החזויים.\n", "\n", "לכן לא ניתן להסיק מהגרף בלבד כי שונות השגיאה קבועה, ונבצע מבחן פורמלי ל-\n", "heteroskedasticity.\n", "\n", "
" ] }, { "cell_type": "markdown", "id": "73c6b474-3566-4237-bd08-e8801585431a", "metadata": {}, "source": [ "### Heteroskedasticity Test\n", "\n", "
\n", "\n", "נשתמש במבחן\n", "Breusch–Pagan\n", "כדי לבדוק האם שונות השגיאות קבועה.\n", "\n", "השערת האפס היא כי קיימת שונות קבועה בשגיאות:\n", "\n", "
\n", "\n", "$$\n", "H_0:\\ Var(\\varepsilon_{it})=\\sigma^2\n", "$$\n", "\n", "
\n", "\n", "לעומת ההשערה החלופית שלפיה שונות השגיאות אינה קבועה.\n", "\n", "אם ערך ה-\n", "p-value\n", "קטן מ-0.05, נדחה את השערת האפס ונקבע שקיימת עדות ל-\n", "heteroskedasticity.\n", "\n", "
" ] }, { "cell_type": "code", "execution_count": 86, "id": "16533e4f-a4e5-474a-b6b0-9f0db32be415", "metadata": { "vscode": { "languageId": "r" } }, "outputs": [ { "data": { "text/plain": [ "\n", "\tBreusch-Pagan test\n", "\n", "data: re_final\n", "BP = 8.956, df = 2, p-value = 0.01136\n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Breusch-Pagan heteroskedasticity test\n", "\n", "hetero_test <- bptest(\n", " re_final,\n", " varformula = ~ fitted(re_final) + I(fitted(re_final)^2),\n", " studentize = FALSE\n", ")\n", "\n", "hetero_test" ] }, { "cell_type": "markdown", "id": "be8c9cee-4855-48a3-b610-1e82e4b928b5", "metadata": {}, "source": [ "
\n", "\n", "במבחן\n", "Breusch–Pagan\n", "התקבל\n", "p-value = 0.0114.\n", "\n", "מכיוון שערך זה קטן מרמת המובהקות של 5%, אנו דוחים את השערת האפס של שונות קבועה בשגיאות.\n", "\n", "לכן קיימת עדות סטטיסטית ל-\n", "heteroskedasticity\n", "בשאריות מודל\n", "Random Effects\n", "הסופי.\n", "\n", "ממצא זה מצביע על\n", "misspecification\n", "במבנה השגיאה, ולכן לאחר השלמת בדיקות השאריות ננסה לתקן את המודל.\n", "\n", "
" ] }, { "cell_type": "markdown", "id": "b8518bb2-0608-4bc7-a18b-35cd328a244b", "metadata": {}, "source": [ "### Normality of Residuals\n", "\n", "
\n", "\n", "בנוסף לבדיקת שונות השגיאות, נבחן האם שאריות המודל מתפלגות בקירוב נורמלית.\n", "\n", "הבדיקה תתבצע באופן גרפי באמצעות\n", "Q-Q Plot\n", "והיסטוגרמת השאריות, ובאופן פורמלי באמצעות מבחן\n", "Jarque–Bera.\n", "\n", "במבחן\n", "JB\n", "השערת האפס היא שהשאריות מתפלגות נורמלית:\n", "\n", "
\n", "\n", "$$\n", "H_0:\\ \\varepsilon_{it}\\sim N(0,\\sigma^2)\n", "$$" ] }, { "cell_type": "code", "execution_count": 90, "id": "2c96f859-05c5-456e-9f55-da4daa1844a7", "metadata": { "vscode": { "languageId": "r" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "Plot with title \"Histogram - Final Random Effects Residuals\"" ] }, "metadata": { "image/png": { "height": 360, "width": 840 } }, "output_type": "display_data" } ], "source": [ "# Normality diagnostics - final Random Effects model\n", "\n", "options(repr.plot.width = 14, repr.plot.height = 6)\n", "\n", "par(mfrow = c(1, 2))\n", "\n", "# Q-Q plot\n", "qqnorm(\n", " res_final,\n", " main = \"Q-Q Plot - Final Random Effects Residuals\"\n", ")\n", "qqline(res_final, col = \"red\")\n", "\n", "# Histogram\n", "hist(\n", " res_final,\n", " breaks = 30,\n", " freq = FALSE,\n", " main = \"Histogram - Final Random Effects Residuals\",\n", " xlab = \"Residuals\"\n", ")\n", "\n", "lines(density(res_final), lwd = 2)\n", "\n", "curve(\n", " dnorm(\n", " x,\n", " mean = mean(res_final),\n", " sd = sd(res_final)\n", " ),\n", " col = \"red\",\n", " lwd = 2,\n", " add = TRUE\n", ")\n", "\n", "par(mfrow = c(1, 1))" ] }, { "cell_type": "code", "execution_count": 92, "id": "e5a8408b-ee07-44d9-8669-916980442cf4", "metadata": { "vscode": { "languageId": "r" } }, "outputs": [ { "data": { "text/plain": [ "\n", "\tJarque Bera Test\n", "\n", "data: res_final\n", "X-squared = 45.233, df = 2, p-value = 1.506e-10\n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Jarque-Bera normality test\n", "\n", "jb_test <- jarque.bera.test(res_final)\n", "\n", "jb_test" ] }, { "cell_type": "markdown", "id": "917538c2-3529-4814-8f42-a215062b899c", "metadata": {}, "source": [ "
\n", "\n", "גרף\n", "Q-Q\n", "מראה כי מרבית השאריות במרכז ההתפלגות נמצאות קרוב לקו התאורטי, אך קיימות סטיות ברורות בזנבות.\n", "\n", "גם ההיסטוגרמה מצביעה על התפלגות דמוית נורמלית במרכז, אך עם זנבות שאינם מתאימים באופן מלא להתפלגות נורמלית.\n", "\n", "במבחן\n", "Jarque–Bera\n", "התקבל\n", "p-value = 1.506×10⁻¹⁰,\n", "ולכן אנו דוחים את השערת האפס של נורמליות השאריות.\n", "\n", "בשילוב עם תוצאת מבחן\n", "Breusch–Pagan,\n", "המסקנה היא כי במודל הסופי קיימת\n", "heteroskedasticity\n", "וכן סטייה מנורמליות השאריות.\n", "\n", " ננסה כעת לתקן את בעיית מבנה השגיאה.\n", "\n", "
" ] }, { "cell_type": "markdown", "id": "69da1ff9-c1a7-4104-b2e9-cfb16a3ac687", "metadata": {}, "source": [ "## 12. Model Correction\n", "\n", "
\n", "\n", "בדיקות השאריות הצביעו על\n", "heteroskedasticity\n", "ועל סטייה מנורמליות.\n", "\n", "מודל\n", "Random Effects\n", "שנבחר באמצעות מבחן\n", "Hausman\n", "נשאר מודל הפאנל המרכזי של הניתוח.\n", "\n", "תחילה נתקן את ההסקה הסטטיסטית באמצעות\n", "robust standard errors,\n", "אשר שומרים על אומדי מודל\n", "RE\n", "אך מתקנים את אומדני אי-הוודאות תחת שונות לא קבועה.\n", "\n", "לאחר מכן נבצע גם ניסיון\n", "FGLS\n", " כדי לבחון האם ניתן לתקן את מבנה השגיאה עצמו.\n", "\n", "
\n", "\n", "### 12.1 Robust Standard Errors" ] }, { "cell_type": "code", "execution_count": 96, "id": "7a6aa359-1b55-4272-8bf3-7a26965ad591", "metadata": { "vscode": { "languageId": "r" } }, "outputs": [ { "data": { "text/plain": [ "\n", "t test of coefficients:\n", "\n", " Estimate Std. Error t value Pr(>|t|) \n", "(Intercept) 4.3349222 0.5830729 7.4346 2.045e-13 ***\n", "lawyes -0.0321184 0.0422381 -0.7604 0.4471648 \n", "male 0.0802377 0.0303041 2.6478 0.0082139 ** \n", "year1978 0.0613298 0.0096669 6.3443 3.208e-10 ***\n", "year1979 0.1690820 0.0159301 10.6140 < 2.2e-16 ***\n", "year1980 0.2245409 0.0245378 9.1508 < 2.2e-16 ***\n", "year1981 0.2265415 0.0271251 8.3517 < 2.2e-16 ***\n", "year1982 0.2059107 0.0300233 6.8584 1.136e-11 ***\n", "year1983 0.1716341 0.0366084 4.6884 3.084e-06 ***\n", "year1984 0.2077843 0.0461139 4.5059 7.285e-06 ***\n", "year1985 0.2606345 0.0554420 4.7010 2.902e-06 ***\n", "year1986 0.3417005 0.0670379 5.0971 4.030e-07 ***\n", "year1987 0.3439705 0.0782419 4.3962 1.203e-05 ***\n", "year1988 0.4091720 0.0846881 4.8315 1.538e-06 ***\n", "year1989 0.4672302 0.0926647 5.0422 5.345e-07 ***\n", "year1990 0.5885509 0.1015500 5.7957 8.783e-09 ***\n", "year1991 0.6443963 0.1077927 5.9781 3.010e-09 ***\n", "year1992 0.6793664 0.1149000 5.9127 4.435e-09 ***\n", "year1993 0.7041200 0.1185816 5.9379 3.822e-09 ***\n", "year1994 0.6932673 0.1231682 5.6286 2.282e-08 ***\n", "year1995 0.6900723 0.1247237 5.5328 3.902e-08 ***\n", "year1996 0.6378846 0.1293843 4.9302 9.425e-07 ***\n", "year1997 0.6203970 0.1317615 4.7085 2.800e-06 ***\n", "year1998 0.5677129 0.1343710 4.2250 2.579e-05 ***\n", "year1999 0.5115120 0.1398877 3.6566 0.0002672 ***\n", "---\n", "Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Robust standard errors for the final Random Effects model\n", "\n", "re_final_robust <- coeftest(\n", " re_final,\n", " vcov = vcovHC(\n", " re_final,\n", " method = \"arellano\",\n", " type = \"HC1\",\n", " cluster = \"group\"\n", " )\n", ")\n", "\n", "re_final_robust" ] }, { "cell_type": "markdown", "id": "25386fe5-17c0-4774-b0ce-d7eafb37f150", "metadata": {}, "source": [ "
\n", "\n", "התיקון אינו משנה את אומדי המקדמים, אלא מתקן את אומדני\n", "Standard Errors\n", "ואת מבחני המובהקות שלהם.\n", "\n", "חישוב מטריצת השונות בוצע בשיטת\n", "Arellano HC1\n", "עם קיבוץ לפי מדינה\n", "(cluster = \"group\").\n", "כך ההסקה עמידה להטרוסקדסטיות ולתלות אפשרית בין תצפיות החוזרות של אותה מדינה לאורך זמן.\n", "\n", "לאחר התיקון, המשתנה\n", "male\n", "נותר מובהק ברמת 1%\n", "(p-value = 0.0082).\n", "\n", "לעומת זאת, המשתנה\n", "law\n", "אינו מובהק לאחר התיקון\n", "(p-value = 0.447).\n", "\n", "לכן, לאחר התחשבות ב-\n", "heteroskedasticity,\n", "אין עדות סטטיסטית מספקת לכך שקיומו של חוק\n", "Shall-Carry\n", "קשור לשיעור הפשיעה האלימה, כאשר יתר המשתנים וההשפעות השנתיות מוחזקים קבועים.\n", "\n", "
" ] }, { "cell_type": "markdown", "id": "a7872b3c-e27c-4c75-837b-86deb2017891", "metadata": {}, "source": [ "### 12.2 FGLS Correction Attempt\n", "\n", "
\n", "\n", "בנוסף לתיקון השגיאות החסינות, ננסה לתקן את\n", "heteroskedasticity\n", "באמצעות\n", "FGLS.\n", "\n", "בשלב הראשון נאמוד את שונות השגיאות באמצעות רגרסיה של ריבועי השאריות על המשתנים המסבירים. השונויות החזויות ישמשו ליצירת משקולות עבור מודל\n", "GLS.\n", "\n", "לאחר מכן נבצע את התהליך באופן איטרטיבי: בכל איטרציה יחושבו שאריות חדשות, יאומד מחדש מודל השונות וייאמד מודל\n", "GLS\n", "חדש. התהליך ייעצר כאשר השינוי בערכים החזויים יהיה קטן מסף ההתכנסות.\n", "\n", "מפרט הממוצע שנשמר הוא:\n", "\n", "
\n", "\n", "$$\n", "\\ln(violent_{it}) =\n", "\\alpha\n", "+ \\beta_1 law_{it}\n", "+ \\beta_2 male_{it}\n", "+ \\sum_{t=1978}^{1999}\\gamma_tD_t\n", "+ \\varepsilon_{it}\n", "$$\n", "\n", "
\n", "\n", "חשוב להדגיש כי\n", "nlme::gls\n", "אינו משחזר את מבנה ה-\n", "Random Effects\n", "של\n", "plm.\n", "לכן ה-\n", "FGLS\n", "ישמש כניסיון לתיקון מבנה השגיאה וכבדיקת עמידות, ולא כתחליף למודל\n", "RE\n", "שנבחר באמצעות\n", "Hausman.\n", "\n", "
" ] }, { "cell_type": "code", "execution_count": 100, "id": "941e54fd-317f-4c26-8665-b36c1f15d157", "metadata": { "vscode": { "languageId": "r" } }, "outputs": [ { "data": { "text/plain": [ "Generalized least squares fit by REML\n", " Model: formula_final \n", " Data: guns \n", " AIC BIC logLik\n", " 2248.032 2379.223 -1098.016\n", "\n", "Variance function:\n", " Structure: fixed weights\n", " Formula: ~fitted_variances \n", "\n", "Coefficients:\n", " Value Std.Error t-value p-value\n", "(Intercept) 5.931822 0.4064717 14.593444 0.0000\n", "lawyes -0.628887 0.0500516 -12.564767 0.0000\n", "male -0.003643 0.0211824 -0.171972 0.8635\n", "year1978 0.046825 0.1383969 0.338336 0.7352\n", "year1979 0.139941 0.1293884 1.081560 0.2797\n", "year1980 0.181533 0.1389156 1.306790 0.1915\n", "year1981 0.177911 0.1420667 1.252308 0.2107\n", "year1982 0.152397 0.1278534 1.191967 0.2335\n", "year1983 0.092945 0.1251154 0.742871 0.4577\n", "year1984 0.100422 0.1239255 0.810342 0.4179\n", "year1985 0.125864 0.1256725 1.001525 0.3168\n", "year1986 0.231324 0.1294442 1.787056 0.0742\n", "year1987 0.221733 0.1304105 1.700272 0.0894\n", "year1988 0.261529 0.1358457 1.925191 0.0545\n", "year1989 0.297933 0.1382404 2.155178 0.0314\n", "year1990 0.429961 0.1396670 3.078471 0.0021\n", "year1991 0.497186 0.1523046 3.264415 0.0011\n", "year1992 0.535944 0.1527217 3.509282 0.0005\n", "year1993 0.543909 0.1528279 3.558964 0.0004\n", "year1994 0.514605 0.1590078 3.236354 0.0012\n", "year1995 0.536088 0.1601129 3.348190 0.0008\n", "year1996 0.523635 0.1648043 3.177315 0.0015\n", "year1997 0.536736 0.1718868 3.122614 0.0018\n", "year1998 0.483226 0.1737865 2.780570 0.0055\n", "year1999 0.425891 0.1832276 2.324384 0.0203\n", "\n", " Correlation: \n", " (Intr) lawyes male yr1978 yr1979 yr1980 yr1981 yr1982 yr1983 yr1984\n", "lawyes 0.063 \n", "male -0.970 -0.072 \n", "year1978 -0.200 -0.001 0.024 \n", "year1979 -0.234 -0.001 0.047 0.554 \n", "year1980 -0.244 -0.005 0.071 0.517 0.554 \n", "year1981 -0.263 -0.007 0.094 0.506 0.543 0.508 \n", "year1982 -0.329 -0.012 0.143 0.563 0.605 0.568 0.559 \n", "year1983 -0.384 -0.014 0.195 0.577 0.621 0.584 0.576 0.647 \n", "year1984 -0.439 -0.017 0.250 0.583 0.629 0.593 0.586 0.661 0.687 \n", "year1985 -0.485 -0.021 0.301 0.577 0.623 0.589 0.583 0.659 0.688 0.711\n", "year1986 -0.524 -0.035 0.347 0.561 0.607 0.575 0.571 0.648 0.679 0.704\n", "year1987 -0.572 -0.042 0.397 0.558 0.605 0.575 0.572 0.651 0.684 0.712\n", "year1988 -0.595 -0.051 0.429 0.537 0.583 0.555 0.554 0.631 0.666 0.695\n", "year1989 -0.625 -0.053 0.463 0.529 0.575 0.549 0.548 0.626 0.663 0.694\n", "year1990 -0.653 -0.067 0.493 0.524 0.571 0.545 0.546 0.625 0.663 0.695\n", "year1991 -0.637 -0.088 0.493 0.482 0.525 0.503 0.504 0.579 0.616 0.648\n", "year1992 -0.662 -0.099 0.519 0.481 0.525 0.504 0.505 0.581 0.619 0.653\n", "year1993 -0.685 -0.100 0.542 0.481 0.526 0.505 0.507 0.584 0.624 0.658\n", "year1994 -0.681 -0.102 0.545 0.463 0.507 0.487 0.490 0.565 0.604 0.639\n", "year1995 -0.695 -0.124 0.560 0.460 0.504 0.485 0.488 0.564 0.604 0.639\n", "year1996 -0.687 -0.151 0.557 0.448 0.490 0.472 0.476 0.550 0.589 0.624\n", "year1997 -0.668 -0.167 0.543 0.429 0.470 0.453 0.457 0.528 0.566 0.601\n", "year1998 -0.665 -0.167 0.542 0.425 0.465 0.449 0.452 0.523 0.561 0.595\n", "year1999 -0.635 -0.162 0.519 0.403 0.442 0.426 0.430 0.497 0.533 0.566\n", " yr1985 yr1986 yr1987 yr1988 yr1989 yr1990 yr1991 yr1992 yr1993 yr1994\n", "lawyes \n", "male \n", "year1978 \n", "year1979 \n", "year1980 \n", "year1981 \n", "year1982 \n", "year1983 \n", "year1984 \n", "year1985 \n", "year1986 0.713 \n", "year1987 0.724 0.724 \n", "year1988 0.709 0.712 0.729 \n", "year1989 0.709 0.714 0.733 0.726 \n", "year1990 0.712 0.719 0.740 0.734 0.742 \n", "year1991 0.665 0.674 0.695 0.691 0.699 0.710 \n", "year1992 0.672 0.681 0.704 0.701 0.710 0.722 0.685 \n", "year1993 0.679 0.689 0.713 0.711 0.721 0.733 0.696 0.709 \n", "year1994 0.659 0.671 0.695 0.693 0.704 0.717 0.681 0.694 0.707 \n", "year1995 0.660 0.673 0.698 0.697 0.708 0.722 0.687 0.701 0.714 0.699\n", "year1996 0.645 0.658 0.683 0.683 0.694 0.708 0.675 0.689 0.702 0.688\n", "year1997 0.622 0.635 0.659 0.660 0.671 0.685 0.653 0.667 0.679 0.666\n", "year1998 0.616 0.629 0.654 0.654 0.665 0.680 0.648 0.662 0.675 0.662\n", "year1999 0.586 0.599 0.622 0.623 0.634 0.647 0.617 0.631 0.643 0.631\n", " yr1995 yr1996 yr1997 yr1998\n", "lawyes \n", "male \n", "year1978 \n", "year1979 \n", "year1980 \n", "year1981 \n", "year1982 \n", "year1983 \n", "year1984 \n", "year1985 \n", "year1986 \n", "year1987 \n", "year1988 \n", "year1989 \n", "year1990 \n", "year1991 \n", "year1992 \n", "year1993 \n", "year1994 \n", "year1995 \n", "year1996 0.696 \n", "year1997 0.675 0.666 \n", "year1998 0.670 0.662 0.642 \n", "year1999 0.639 0.631 0.613 0.608\n", "\n", "Standardized residuals:\n", " Min Q1 Med Q3 Max \n", "-4.85061172 -0.68650114 0.08388317 0.64867876 3.16665748 \n", "\n", "Residual standard error: 4.462034 \n", "Degrees of freedom: 1173 total; 1148 residual" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Initial variance estimation for FGLS\n", "\n", "fgls_residuals <- as.numeric(resid(re_final))\n", "\n", "variance_model <- lm(\n", " I(fgls_residuals^2) ~ law + male + year,\n", " data = guns\n", ")\n", "\n", "fitted_variances <- fitted(variance_model)\n", "\n", "# Initial FGLS model\n", "\n", "fgls_model <- gls(\n", " formula_final,\n", " data = guns,\n", " weights = varFixed(~ fitted_variances)\n", ")\n", "\n", "summary(fgls_model)" ] }, { "cell_type": "code", "execution_count": 102, "id": "4aa729a4-0872-4e5c-b1e7-a5c2aa6e39b8", "metadata": { "vscode": { "languageId": "r" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "FGLS converged: TRUE \n", "Iterations: 4 \n" ] }, { "data": { "text/plain": [ "Generalized least squares fit by REML\n", " Model: formula_final \n", " Data: guns \n", " AIC BIC logLik\n", " 2186.015 2317.206 -1067.008\n", "\n", "Variance function:\n", " Structure: fixed weights\n", " Formula: ~new_fitted_variances \n", "\n", "Coefficients:\n", " Value Std.Error t-value p-value\n", "(Intercept) 5.951096 0.3662082 16.250579 0.0000\n", "lawyes -0.572184 0.0494083 -11.580718 0.0000\n", "male -0.004863 0.0190158 -0.255711 0.7982\n", "year1978 0.043754 0.1055869 0.414391 0.6787\n", "year1979 0.138793 0.1072453 1.294161 0.1959\n", "year1980 0.172222 0.1119700 1.538105 0.1243\n", "year1981 0.176699 0.1141802 1.547545 0.1220\n", "year1982 0.152302 0.1141714 1.333979 0.1825\n", "year1983 0.092030 0.1136883 0.809498 0.4184\n", "year1984 0.098869 0.1136004 0.870326 0.3843\n", "year1985 0.123706 0.1167834 1.059273 0.2897\n", "year1986 0.232995 0.1149612 2.026731 0.0429\n", "year1987 0.222274 0.1168760 1.901796 0.0574\n", "year1988 0.259369 0.1245074 2.083163 0.0375\n", "year1989 0.295060 0.1274664 2.314809 0.0208\n", "year1990 0.423358 0.1288597 3.285416 0.0010\n", "year1991 0.493524 0.1329387 3.712418 0.0002\n", "year1992 0.527487 0.1332092 3.959842 0.0001\n", "year1993 0.532652 0.1351680 3.940663 0.0001\n", "year1994 0.500777 0.1369612 3.656343 0.0003\n", "year1995 0.511079 0.1394336 3.665394 0.0003\n", "year1996 0.483604 0.1426299 3.390619 0.0007\n", "year1997 0.482170 0.1438557 3.351759 0.0008\n", "year1998 0.426869 0.1425262 2.995023 0.0028\n", "year1999 0.358937 0.1424469 2.519797 0.0119\n", "\n", " Correlation: \n", " (Intr) lawyes male yr1978 yr1979 yr1980 yr1981 yr1982 yr1983 yr1984\n", "lawyes 0.097 \n", "male -0.979 -0.105 \n", "year1978 -0.178 -0.004 0.037 \n", "year1979 -0.207 -0.008 0.069 0.485 \n", "year1980 -0.236 -0.013 0.104 0.466 0.463 \n", "year1981 -0.263 -0.017 0.135 0.459 0.456 0.442 \n", "year1982 -0.308 -0.027 0.181 0.460 0.459 0.447 0.444 \n", "year1983 -0.359 -0.031 0.233 0.464 0.464 0.454 0.453 0.463 \n", "year1984 -0.412 -0.036 0.286 0.467 0.469 0.460 0.460 0.473 0.490 \n", "year1985 -0.453 -0.042 0.332 0.456 0.459 0.453 0.455 0.470 0.489 0.507\n", "year1986 -0.511 -0.056 0.389 0.465 0.470 0.465 0.469 0.487 0.509 0.530\n", "year1987 -0.555 -0.066 0.437 0.459 0.466 0.463 0.469 0.489 0.513 0.537\n", "year1988 -0.569 -0.074 0.458 0.433 0.441 0.440 0.447 0.468 0.493 0.518\n", "year1989 -0.595 -0.077 0.488 0.424 0.434 0.434 0.442 0.464 0.491 0.517\n", "year1990 -0.623 -0.093 0.518 0.421 0.431 0.433 0.442 0.466 0.494 0.522\n", "year1991 -0.641 -0.111 0.541 0.410 0.421 0.424 0.433 0.458 0.488 0.517\n", "year1992 -0.668 -0.123 0.567 0.410 0.422 0.426 0.436 0.463 0.493 0.524\n", "year1993 -0.683 -0.124 0.584 0.405 0.418 0.422 0.434 0.460 0.492 0.524\n", "year1994 -0.697 -0.126 0.600 0.401 0.414 0.419 0.431 0.459 0.491 0.524\n", "year1995 -0.706 -0.149 0.612 0.394 0.408 0.414 0.426 0.455 0.488 0.521\n", "year1996 -0.704 -0.177 0.612 0.386 0.400 0.407 0.419 0.447 0.480 0.513\n", "year1997 -0.709 -0.196 0.618 0.383 0.397 0.404 0.417 0.446 0.479 0.512\n", "year1998 -0.719 -0.195 0.628 0.387 0.401 0.409 0.421 0.451 0.484 0.518\n", "year1999 -0.724 -0.195 0.633 0.387 0.402 0.409 0.422 0.452 0.486 0.520\n", " yr1985 yr1986 yr1987 yr1988 yr1989 yr1990 yr1991 yr1992 yr1993 yr1994\n", "lawyes \n", "male \n", "year1978 \n", "year1979 \n", "year1980 \n", "year1981 \n", "year1982 \n", "year1983 \n", "year1984 \n", "year1985 \n", "year1986 0.536 \n", "year1987 0.546 0.577 \n", "year1988 0.528 0.561 0.576 \n", "year1989 0.529 0.563 0.581 0.569 \n", "year1990 0.535 0.571 0.590 0.579 0.586 \n", "year1991 0.532 0.569 0.589 0.579 0.588 0.601 \n", "year1992 0.540 0.579 0.600 0.591 0.601 0.615 0.619 \n", "year1993 0.541 0.580 0.603 0.594 0.604 0.619 0.624 0.639 \n", "year1994 0.541 0.582 0.605 0.597 0.608 0.623 0.628 0.644 0.650 \n", "year1995 0.539 0.581 0.605 0.598 0.609 0.625 0.631 0.647 0.653 0.659\n", "year1996 0.532 0.573 0.598 0.591 0.602 0.619 0.625 0.642 0.649 0.655\n", "year1997 0.531 0.573 0.598 0.592 0.603 0.620 0.627 0.645 0.651 0.657\n", "year1998 0.538 0.580 0.605 0.599 0.611 0.628 0.635 0.653 0.659 0.665\n", "year1999 0.539 0.582 0.608 0.602 0.613 0.631 0.638 0.656 0.662 0.668\n", " yr1995 yr1996 yr1997 yr1998\n", "lawyes \n", "male \n", "year1978 \n", "year1979 \n", "year1980 \n", "year1981 \n", "year1982 \n", "year1983 \n", "year1984 \n", "year1985 \n", "year1986 \n", "year1987 \n", "year1988 \n", "year1989 \n", "year1990 \n", "year1991 \n", "year1992 \n", "year1993 \n", "year1994 \n", "year1995 \n", "year1996 0.659 \n", "year1997 0.662 0.660 \n", "year1998 0.671 0.668 0.672 \n", "year1999 0.674 0.671 0.675 0.684\n", "\n", "Standardized residuals:\n", " Min Q1 Med Q3 Max \n", "-3.9883730 -0.7385098 0.1140182 0.6886200 2.8138803 \n", "\n", "Residual standard error: 1.011053 \n", "Degrees of freedom: 1173 total; 1148 residual" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Iterate FGLS until convergence\n", "\n", "tolerance <- 1e-6\n", "max_iterations <- 10\n", "iteration <- 1\n", "converged <- FALSE\n", "\n", "while (iteration <= max_iterations & !converged) {\n", "\n", " # Update residuals\n", " fgls_residuals <- residuals(fgls_model)\n", "\n", " # Re-estimate the variance model\n", " variance_model <- lm(\n", " I(fgls_residuals^2) ~ law + male + year,\n", " data = guns\n", " )\n", "\n", " new_fitted_variances <- fitted(variance_model)\n", "\n", " # Re-estimate FGLS with updated variance estimates\n", " new_fgls_model <- gls(\n", " formula_final,\n", " data = guns,\n", " weights = varFixed(~ new_fitted_variances)\n", " )\n", "\n", " # Check convergence\n", " if (sum((fitted(new_fgls_model) - fitted(fgls_model))^2) < tolerance) {\n", " converged <- TRUE\n", " }\n", "\n", " # Update\n", " fgls_model <- new_fgls_model\n", " fitted_variances <- new_fitted_variances\n", " iteration <- iteration + 1\n", "}\n", "\n", "cat(\"FGLS converged:\", converged, \"\\n\")\n", "cat(\"Iterations:\", iteration - 1, \"\\n\")\n", "\n", "summary(fgls_model)" ] }, { "cell_type": "code", "execution_count": 104, "id": "88620cb6-cf03-4eab-b032-83d10e4c1d8d", "metadata": { "vscode": { "languageId": "r" } }, "outputs": [ { "data": { "text/html": [ "\n", "
  1. 0.0766755000180978
  2. 0.652228567954739
\n" ], "text/latex": [ "\\begin{enumerate*}\n", "\\item 0.0766755000180978\n", "\\item 0.652228567954739\n", "\\end{enumerate*}\n" ], "text/markdown": [ "1. 0.0766755000180978\n", "2. 0.652228567954739\n", "\n", "\n" ], "text/plain": [ "[1] 0.0766755 0.6522286" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "0" ], "text/latex": [ "0" ], "text/markdown": [ "0" ], "text/plain": [ "[1] 0" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Check the estimated variance function\n", "\n", "range(new_fitted_variances)\n", "sum(new_fitted_variances <= 0)" ] }, { "cell_type": "markdown", "id": "69f65260-1948-4cff-99e2-1564bac6c7ac", "metadata": {}, "source": [ "
\n", "\n", "אומדני השונות שהתקבלו ממודל השונות נמצאים בטווח\n", "0.077–0.652,\n", "ולא התקבלו אומדני שונות שליליים.\n", "\n", "לכן פונקציית השונות ששימשה ליצירת המשקולות ב-\n", "FGLS\n", "תקינה מבחינה בסיסית, וניתן להמשיך ולבדוק האם האמידה המשוקללת אכן שיפרה את התנהגות השאריות.\n", "\n", "
" ] }, { "cell_type": "markdown", "id": "a463deab-dd4c-493e-89bd-4ec0b561203a", "metadata": {}, "source": [ "### 12.3 FGLS Residual Diagnostics\n", "\n", "
\n", "\n", "כדי לבדוק האם תיקון\n", "FGLS\n", "הצליח לצמצם את ה-\n", "heteroskedasticity,\n", "נבחן מחדש את השאריות לאחר האמידה המשוקללת.\n", "\n", "נשתמש בשאריות המנורמלות של מודל\n", "FGLS,\n", "ונבצע מחדש את גרף\n", "Residuals vs Fitted\n", "ואת מבחן\n", "Breusch–Pagan.\n", "\n", "
" ] }, { "cell_type": "code", "execution_count": 108, "id": "971586ca-81e4-4fa9-8c0c-b8ea64c6c56a", "metadata": { "vscode": { "languageId": "r" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "Plot with title \"Residuals vs Fitted - FGLS Model\"" ] }, "metadata": { "image/png": { "height": 420, "width": 720 } }, "output_type": "display_data" } ], "source": [ "# FGLS residual diagnostics\n", "\n", "res_fgls <- as.numeric(residuals(fgls_model, type = \"normalized\"))\n", "fit_fgls <- as.numeric(fitted(fgls_model))\n", "\n", "options(repr.plot.width = 12, repr.plot.height = 7)\n", "\n", "plot(\n", " fit_fgls,\n", " res_fgls,\n", " main = \"Residuals vs Fitted - FGLS Model\",\n", " xlab = \"Fitted Values\",\n", " ylab = \"Normalized Residuals\",\n", " pch = 20\n", ")\n", "\n", "abline(h = 0, col = \"red\")" ] }, { "cell_type": "code", "execution_count": 110, "id": "050a113d-d784-41a1-81e2-fd8b78299163", "metadata": { "vscode": { "languageId": "r" } }, "outputs": [ { "data": { "text/plain": [ "\n", "\tBreusch-Pagan test\n", "\n", "data: res_fgls ~ fit_fgls + I(fit_fgls^2)\n", "BP = 10.722, df = 2, p-value = 0.004695\n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Breusch-Pagan test after FGLS\n", "\n", "hetero_test_fgls <- bptest(\n", " res_fgls ~ fit_fgls + I(fit_fgls^2),\n", " studentize = FALSE\n", ")\n", "\n", "hetero_test_fgls" ] }, { "cell_type": "markdown", "id": "4f82bc15-4464-49a6-b9cd-3740fadb2ede", "metadata": {}, "source": [ "
\n", "\n", "מודל\n", "FGLS\n", "התכנס לאחר 4 איטרציות, אך בדיקת השאריות מראה כי תיקון ההטרוסקדסטיות לא הצליח.\n", "\n", "במבחן\n", "Breusch–Pagan\n", "לאחר\n", "FGLS\n", "התקבל\n", "p-value = 0.0047.\n", "\n", "מכיוון שערך זה קטן מ-0.05, אנו עדיין דוחים את השערת האפס של שונות קבועה בשגיאות.\n", "\n", "לכן, למרות שהאלגוריתם התכנס והמשקולות התבססו על אומדני שונות חיוביים, מודל\n", "FGLS\n", "לא הצליח להסיר את ה-\n", "heteroskedasticity\n", "מהשאריות.\n", "\n", "בהתאם לכך, תוצאות מודל\n", "Random Effects\n", "עם\n", "robust standard errors\n", "יישארו הבסיס המרכזי להסקה הסטטיסטית, בעוד שה-\n", "FGLS\n", "יוצג כניסיון נוסף לתיקון מבנה השגיאה שלא פתר את הבעיה במלואה.\n", "\n", "
" ] }, { "cell_type": "markdown", "id": "98a2e853-cdce-4f8f-b354-0ee73fae28ff", "metadata": {}, "source": [ "### 12.4 Normality after FGLS\n", "\n", "
\n", "\n", "נבחן גם האם אמידת\n", "FGLS\n", "שיפרה את נורמליות השאריות באמצעות\n", "Q-Q Plot,\n", "היסטוגרמה ומבחן\n", "Jarque–Bera.\n", "\n", "
" ] }, { "cell_type": "code", "execution_count": 114, "id": "c298c09f-6e47-46e7-a61f-f27e5b08451c", "metadata": { "vscode": { "languageId": "r" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "Plot with title \"Histogram - FGLS Residuals\"" ] }, "metadata": { "image/png": { "height": 360, "width": 840 } }, "output_type": "display_data" } ], "source": [ "# Normality diagnostics after FGLS\n", "\n", "options(repr.plot.width = 14, repr.plot.height = 6)\n", "\n", "par(mfrow = c(1, 2))\n", "\n", "qqnorm(\n", " res_fgls,\n", " main = \"Q-Q Plot - FGLS Residuals\"\n", ")\n", "qqline(res_fgls, col = \"red\")\n", "\n", "hist(\n", " res_fgls,\n", " breaks = 30,\n", " freq = FALSE,\n", " main = \"Histogram - FGLS Residuals\",\n", " xlab = \"Normalized Residuals\"\n", ")\n", "\n", "lines(density(res_fgls), lwd = 2)\n", "\n", "curve(\n", " dnorm(\n", " x,\n", " mean = mean(res_fgls),\n", " sd = sd(res_fgls)\n", " ),\n", " col = \"red\",\n", " lwd = 2,\n", " add = TRUE\n", ")\n", "\n", "par(mfrow = c(1, 1))" ] }, { "cell_type": "code", "execution_count": 116, "id": "41635dd2-8de8-42eb-bcf7-5579cd068a10", "metadata": { "vscode": { "languageId": "r" } }, "outputs": [ { "data": { "text/plain": [ "\n", "\tJarque Bera Test\n", "\n", "data: res_fgls\n", "X-squared = 44.837, df = 2, p-value = 1.836e-10\n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Jarque-Bera test after FGLS\n", "\n", "jb_test_fgls <- jarque.bera.test(res_fgls)\n", "\n", "jb_test_fgls" ] }, { "cell_type": "markdown", "id": "7e87b91f-9d7c-4908-8dbe-a09b51209854", "metadata": {}, "source": [ "
\n", "\n", "גם לאחר אמידת\n", "FGLS\n", "מבחן\n", "Jarque–Bera\n", "דוחה את השערת הנורמליות, עם\n", "p-value = 1.836×10⁻¹⁰.\n", "\n", "גם מבחינה גרפית, גרף\n", "Q-Q\n", "מצביע על התאמה סבירה יחסית במרכז ההתפלגות, אך על סטיות ברורות בזנבות.\n", "\n", "בנוסף, מבחן\n", "Breusch–Pagan\n", "שבוצע לאחר\n", "FGLS\n", "התקבל עם\n", "p-value = 0.0047,\n", "ולכן גם בעיית ה-\n", "heteroskedasticity\n", "לא נפתרה.\n", "\n", "לפיכך, אף שמודל\n", "FGLS\n", "התכנס לאחר ארבע איטרציות והשתמש באומדני שונות חיוביים, ניסיון התיקון לא הצליח להביא לקיום מלא של הנחות השגיאה.\n", "\n", "בהתאם לכך, מודל\n", "Random Effects\n", "נשאר המודל המרכזי של הניתוח, וההסקה הסטטיסטית ממנו תתבסס על\n", "robust standard errors\n", "כדי להתמודד עם ההטרוסקדסטיות.\n", "\n", "
" ] }, { "cell_type": "markdown", "id": "fe578566-b8f8-43f3-8b68-ada0d01a0a3f", "metadata": {}, "source": [ "## 13. Final Results and Conclusions\n", "\n", "
\n", "\n", "בשלב הראשון נאמדו מודלי\n", "Fixed Effects\n", "ו-Random Effects\n", "על אותו מפרט.\n", "\n", "לאחר טיפול ב-\n", "multicollinearity\n", "בין\n", "log_population\n", "ו-log_density,\n", "בוצע מבחן\n", "Hausman.\n", "במבחן התקבל\n", "p-value = 0.0892,\n", "ולכן ברמת מובהקות של 5% לא דחינו את השערת האפס ובחרנו במודל\n", "Random Effects.\n", "\n", "לאחר בחירת המודל בוצע סינון הדרגתי של המשתנים המסבירים. המודל הסופי שהתקבל הוא:\n", "\n", "
\n", "\n", "$$\n", "\\ln(violent_{it}) =\n", "\\alpha\n", "+ \\beta_1 law_{it}\n", "+ \\beta_2 male_{it}\n", "+ \\sum_{t=1978}^{1999}\\gamma_tD_t\n", "+ \\mu_i\n", "+ \\varepsilon_{it}\n", "$$\n", "\n", "
\n", "\n", "במודל\n", "Random Effects\n", "הסופי התקבל עבור\n", "law\n", "מקדם של\n", "-0.0321.\n", "\n", "אומדן נקודתי זה מתאים בקירוב לירידה של כ-3.16% בשיעור הפשיעה האלימה כאשר חוק\n", "Shall-Carry\n", "בתוקף.\n", "\n", "עם זאת, לאחר שנמצאה\n", "heteroskedasticity\n", "וחושבו\n", "robust standard errors,\n", "התקבל עבור\n", "law\n", "ערך\n", "p-value = 0.447.\n", "\n", "לכן אין עדות סטטיסטית מספקת לכך שקיומו של חוק\n", "Shall-Carry\n", "קשור לשינוי בשיעור הפשיעה האלימה. כלומר, אין לפרש את הירידה הנקודתית של כ-3.16% כהשפעה מובהקת.\n", "\n", "עבור\n", "male\n", "התקבל מקדם של\n", "0.0802,\n", "והמשתנה נשאר מובהק גם לאחר תיקון השגיאות\n", "(p-value = 0.0082).\n", "\n", "מכיוון שהמשתנה המוסבר נמצא בסקאלה לוגריתמית, עלייה של נקודת אחוז אחת ב-\n", "male\n", "קשורה בקירוב לעלייה של כ-8% בשיעור הפשיעה האלימה, בהינתן יתר המשתנים במודל.\n", "\n", "גם משתני השנה מצביעים על שינויים משמעותיים בשיעור הפשיעה האלימה לאורך תקופת המדגם ביחס לשנת הבסיס 1977.\n", "\n", "למודל התקבל\n", "R² = 0.399\n", "\n", "
" ] } ], "metadata": { "kernelspec": { "display_name": "R", "language": "R", "name": "ir" }, "language_info": { "codemirror_mode": "r", "file_extension": ".r", "mimetype": "text/x-r-source", "name": "R", "pygments_lexer": "r", "version": "4.5.1" } }, "nbformat": 4, "nbformat_minor": 5 }