## Loading required package: car
## Loading required package: carData
## Loading required package: lmtest
## Loading required package: zoo
##
## Attaching package: 'zoo'
## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric
## Loading required package: sandwich
## Loading required package: survival
## Registered S3 methods overwritten by 'lme4':
## method from
## cooks.distance.influence.merMod car
## influence.merMod car
## dfbeta.influence.merMod car
## dfbetas.influence.merMod car
## district school county grades students teachers
## 1 75119 Sunol Glen Unified Alameda KK-08 195 10.90
## 2 61499 Manzanita Elementary Butte KK-08 240 11.15
## 3 61549 Thermalito Union Elementary Butte KK-08 1550 82.90
## 4 61457 Golden Feather Union Elementary Butte KK-08 243 14.00
## 5 61523 Palermo Union Elementary Butte KK-08 1335 71.50
## 6 62042 Burrel Union Elementary Fresno KK-08 137 6.40
## calworks lunch computer expenditure income english read math
## 1 0.5102 2.0408 67 6384.911 22.690001 0.000000 691.6 690.0
## 2 15.4167 47.9167 101 5099.381 9.824000 4.583333 660.5 661.9
## 3 55.0323 76.3226 169 5501.955 8.978000 30.000002 636.3 650.9
## 4 36.4754 77.0492 85 7101.831 8.978000 0.000000 651.9 643.5
## 5 33.1086 78.4270 171 5235.988 9.080333 13.857677 641.8 639.9
## 6 12.3188 86.9565 25 5580.147 10.415000 12.408759 605.7 605.4
## district school county grades
## Length:420 Length:420 Sonoma : 29 KK-06: 61
## Class :character Class :character Kern : 27 KK-08:359
## Mode :character Mode :character Los Angeles: 27
## Tulare : 24
## San Diego : 21
## Santa Clara: 20
## (Other) :272
## students teachers calworks lunch
## Min. : 81.0 Min. : 4.85 Min. : 0.000 Min. : 0.00
## 1st Qu.: 379.0 1st Qu.: 19.66 1st Qu.: 4.395 1st Qu.: 23.28
## Median : 950.5 Median : 48.56 Median :10.520 Median : 41.75
## Mean : 2628.8 Mean : 129.07 Mean :13.246 Mean : 44.71
## 3rd Qu.: 3008.0 3rd Qu.: 146.35 3rd Qu.:18.981 3rd Qu.: 66.86
## Max. :27176.0 Max. :1429.00 Max. :78.994 Max. :100.00
##
## computer expenditure income english
## Min. : 0.0 Min. :3926 Min. : 5.335 Min. : 0.000
## 1st Qu.: 46.0 1st Qu.:4906 1st Qu.:10.639 1st Qu.: 1.941
## Median : 117.5 Median :5215 Median :13.728 Median : 8.778
## Mean : 303.4 Mean :5312 Mean :15.317 Mean :15.768
## 3rd Qu.: 375.2 3rd Qu.:5601 3rd Qu.:17.629 3rd Qu.:22.970
## Max. :3324.0 Max. :7712 Max. :55.328 Max. :85.540
##
## read math
## Min. :604.5 Min. :605.4
## 1st Qu.:640.4 1st Qu.:639.4
## Median :655.8 Median :652.5
## Mean :655.0 Mean :653.3
## 3rd Qu.:668.7 3rd Qu.:665.9
## Max. :704.0 Max. :709.5
##
## 'data.frame': 420 obs. of 14 variables:
## $ district : chr "75119" "61499" "61549" "61457" ...
## $ school : chr "Sunol Glen Unified" "Manzanita Elementary" "Thermalito Union Elementary" "Golden Feather Union Elementary" ...
## $ county : Factor w/ 45 levels "Alameda","Butte",..: 1 2 2 2 2 6 29 11 6 25 ...
## $ grades : Factor w/ 2 levels "KK-06","KK-08": 2 2 2 2 2 2 2 2 2 1 ...
## $ students : num 195 240 1550 243 1335 ...
## $ teachers : num 10.9 11.1 82.9 14 71.5 ...
## $ calworks : num 0.51 15.42 55.03 36.48 33.11 ...
## $ lunch : num 2.04 47.92 76.32 77.05 78.43 ...
## $ computer : num 67 101 169 85 171 25 28 66 35 0 ...
## $ expenditure: num 6385 5099 5502 7102 5236 ...
## $ income : num 22.69 9.82 8.98 8.98 9.08 ...
## $ english : num 0 4.58 30 0 13.86 ...
## $ read : num 692 660 636 652 642 ...
## $ math : num 690 662 651 644 640 ...
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 683.45305948 9.56214469 71.4748711 3.011667e-218
## stratio -0.30035544 0.25797023 -1.1643027 2.450536e-01
## english -0.20550107 0.03765408 -5.4576041 8.871666e-08
## lunch -0.38684059 0.03700982 -10.4523759 1.427370e-22
## gradesKK-08 -1.91291321 1.35865394 -1.4079474 1.599886e-01
## income 0.71615378 0.09832843 7.2832829 1.986712e-12
## calworks -0.05273312 0.06154758 -0.8567863 3.921191e-01
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 700.47891593 13.58064436 51.5792106 8.950497e-171
## stratio -1.13674002 0.53533638 -2.1234126 3.438427e-02
## english -0.21396934 0.03847833 -5.5607753 5.162571e-08
## lunch -0.39384225 0.03773637 -10.4366757 1.621794e-22
## gradesKK-08 -1.89227865 1.37791820 -1.3732881 1.704966e-01
## income 0.62487986 0.11199008 5.5797785 4.668490e-08
## calworks -0.04950501 0.06244410 -0.7927892 4.284101e-01
## No start parameters were given. The linear model read ~ stratio is fitted to derive them.
## The start parameters c((Intercept)=706.449, stratio=-2.621, pi1=19.64, pi2=21.532, theta5=0.5, theta6=1, theta7=0.5, theta8=1) are used for optimization.
## Estimate Std. Error z-score Pr(>|z|)
## (Intercept) 6.996014e+02 2.686186e+02 2.604441e+00 9.529597e-03
## stratio -2.272673e+00 1.367757e+01 -1.661605e-01 8.681108e-01
## pi1 -4.896363e+01 5.526907e-08 -8.859139e+08 0.000000e+00
## pi2 1.963920e+01 9.225351e-02 2.128830e+02 0.000000e+00
## theta5 6.939432e-152 3.354672e-160 2.068587e+08 0.000000e+00
## theta6 3.787512e+02 4.249457e+01 8.912932e+00 1.541524e-17
## theta7 -1.227543e+00 4.885276e+01 -2.512741e-02 9.799653e-01
## Warning: It is recommended to run 1000 or more bootstraps.
## Point Estimate Boots SE Lower Boots CI (95%)
## (Intercept) 682.56562449 2.892541893 NA
## stratio -0.40322352 0.188960137 NA
## english -0.20380742 0.010970833 NA
## lunch -0.36426215 0.031529433 NA
## calworks -0.07186591 0.003223237 NA
## gradesKK-08 -0.72045639 0.195490165 NA
## income 0.78911122 0.040396762 NA
## Upper Boots CI (95%)
## (Intercept) NA
## stratio NA
## english NA
## lunch NA
## calworks NA
## gradesKK-08 NA
## income NA
## Residuals were derived by fitting stratio ~ english + lunch + calworks + income + grades + county.
## The following internal instruments were built: IIV(income), IIV(english).
## Fitting an instrumental variable regression with model read ~ stratio + english + lunch + calworks + income + grades + |english + lunch + calworks + income + grades + county + IIV(income) + IIV(english) county|english + lunch + calworks + income + grades + county + IIV(income) + IIV(english).
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 662.78791557 27.90173069 23.7543657 2.380436e-76
## stratio 0.71480686 1.31077325 0.5453322 5.858545e-01
## english -0.19522271 0.04057527 -4.8113717 2.188618e-06
## lunch -0.37834232 0.03927793 -9.6324402 9.760809e-20
## calworks -0.05665126 0.06302095 -0.8989273 3.692776e-01
## income 0.82693755 0.17236557 4.7975797 2.335271e-06
## gradesKK-08 -1.93795843 1.38723186 -1.3969968 1.632541e-01
## The following internal instruments were built: IIV(iiv=gp,g=x3,income).
## Fitting an instrumental variable regression with model read ~ stratio + english + lunch + calworks + income + grades + |english + lunch + calworks + income + grades + county + IIV(iiv=gp,g=x3,income) county|english + lunch + calworks + income + grades + county + IIV(iiv=gp,g=x3,income).
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 703.95605932 56.18284961 12.5297322 2.974075e-30
## stratio -1.30755252 2.73072188 -0.4788304 6.323429e-01
## english -0.21569879 0.04726222 -4.5638738 6.848861e-06
## lunch -0.39527218 0.04409111 -8.9648953 1.576520e-17
## calworks -0.04884574 0.06367608 -0.7670971 4.435143e-01
## income 0.60623924 0.31312518 1.9360923 5.361980e-02
## gradesKK-08 -1.88806451 1.38805414 -1.3602240 1.745894e-01
## Fitting linear mixed-effects model.
## Detected multilevel model with 2 levels.
## For county (Level 2), 45 groups were found.
## Estimate Std. Error z-score Pr(>|z|)
## (Intercept) 675.8228656 5.58008680 121.1133248 0.000000e+00
## stratio -0.4956054 0.23922638 -2.0717005 3.829339e-02
## english -0.2599777 0.03413530 -7.6160948 2.614656e-14
## lunch -0.3692954 0.03560210 -10.3728537 3.295342e-25
## income 0.6723141 0.08862012 7.5864728 3.287314e-14
## gr08TRUE 2.1590333 1.28167222 1.6845440 9.207658e-02
## calworks -0.0570633 0.05711701 -0.9990596 3.177658e-01