Recently there have been momentum in the discussion of international assessments. One of such assessment is the Trends in International Mathematics and Science Study (TIMSS). TIMSS is a globally recognized test measuring both maximum performance behaviors as well as typical performance behaviors of students in fourth, eighth, and twelve grades (TIMSS & PIRLS International Study Center, 2018). Specifically, TIMSS measures students’ achievement in mathematics and sciences. There are accompanied assessments that solicit information about students’ backgrounds, attitudes, and perceptions about mathematics, sciences, and their respective teachers and schools. TIMSS also collects data about teachers’ attitudes toward their students and schools’ environments as well as the subject-matters and curricula being implemented. TIMSS gather data from school administrators (TIMSS & PIRLS International Study Center, 2018).
Reading the Data
library(foreign)
library(reshape)
library(reshape2)
##
## Attaching package: 'reshape2'
## The following objects are masked from 'package:reshape':
##
## colsplit, melt, recast
library(lme4)
## Loading required package: Matrix
##
## Attaching package: 'Matrix'
## The following object is masked from 'package:reshape':
##
## expand
library(sjstats)
library(rockchalk)
library(lattice)
library(ggplot2)
library(psych)
##
## Attaching package: 'psych'
## The following objects are masked from 'package:ggplot2':
##
## %+%, alpha
## The following objects are masked from 'package:sjstats':
##
## pca, phi
setwd("/Users/yahyaalshehri/Desktop/SAudi TIMSS")
###sss<- read.spss("asgsaum652.sav", to.data.frame = TRUE)
dtfile <- read.csv("TIMSS.csv")[,c("IDSCHOOL", "IDBOOK", "ITSEX","ASBM01A", "ASBM01B", "ASBM01C", "ASBM01D","ASBM01E",
"ASBM01F", "ASBM01G", "ASBM01H","ASBM01I","ASMMAT03")]
# I enjoy learning mathematics
# I wish I did not have to study mathematics
# Mathematics is boring
# I learn many interesting things in mathematics
# I like mathematics
# I like any schoolwork that involves numbers
# I like to solve mathematics problems
# I look forward to mathematics lessons
# Mathematics is one of my favorite subjects
head(dtfile)
## IDSCHOOL IDBOOK ITSEX ASBM01A ASBM01B ASBM01C ASBM01D ASBM01E ASBM01F
## 1 1 9 1 1 4 4 2 2 2
## 2 1 10 1 1 4 4 2 2 2
## 3 1 11 1 1 4 4 2 2 2
## 4 1 12 1 1 4 4 2 2 2
## 5 1 13 1 2 4 4 2 2 2
## 6 1 14 1 1 4 4 2 2 2
## ASBM01G ASBM01H ASBM01I ASMMAT03
## 1 2 2 3 374.9874
## 2 2 1 2 541.6871
## 3 2 1 1 427.7202
## 4 2 2 1 525.5990
## 5 2 2 2 452.4498
## 6 NA 2 1 539.5486
colnames(dtfile)
## [1] "IDSCHOOL" "IDBOOK" "ITSEX" "ASBM01A" "ASBM01B" "ASBM01C"
## [7] "ASBM01D" "ASBM01E" "ASBM01F" "ASBM01G" "ASBM01H" "ASBM01I"
## [13] "ASMMAT03"
dtfile$IDSCHOOL <- as.factor(dtfile$IDSCHOOL)
dtfile$IDBOOK <- as.factor(dtfile$IDBOOK)
dtfile$Gender <- factor(dtfile$ITSEX)
dtfile$Gender <- factor(dtfile$ITSEX, levels = c(2,1), labels= c ("Male", "Female"))
with(dtfile, table(Gender, ITSEX))
## ITSEX
## Gender 1 2
## Male 0 2156
## Female 2181 0
Summarize the Data
rockchalk::summarize(dtfile)
## Numeric variables
## ITSEX ASBM01A ASBM01B ASBM01C ASBM01D ASBM01E
## min 1 1 1 1 1 1
## med 1 1 4 4 1 1
## max 2 9 9 9 9 9
## mean 1.50 1.68 3.37 3.49 2 2
## sd 0.50 1.59 1.85 1.93 2.12 2.09
## skewness 0.01 3.32 1.18 1.22 2.55 2.54
## kurtosis -2 11.80 2.59 2.29 5.52 5.60
## nobs 4337 4225 4236 4242 4252 4263
## nmissing 0 112 101 95 85 74
## ASBM01F ASBM01G ASBM01H ASBM01I ASMMAT03
## min 1 1 1 1 40.78
## med 1 1 1 1 384.41
## max 9 9 9 9 722.22
## mean 2.05 2.04 2.14 2.13 384.26
## sd 2.08 2.08 2.11 2.02 90.28
## skewness 2.55 2.53 2.36 2.35 -0.03
## kurtosis 5.68 5.62 4.85 5.18 -0.12
## nobs 4268 4269 4269 4282 4337
## nmissing 69 68 68 55 0
##
## Nonnumeric variables
## IDSCHOOL IDBOOK Gender
## 116 : 44 3 : 324 Female: 2181
## 84 : 43 9 : 321 Male : 2156
## 11 : 40 4 : 318 nobs : 4337
## 183 : 40 1 : 314 nmiss : 0
## (All Others): 4170 (All Others): 3060 entropy : 1
## nobs : 4337 nobs : 4337 normedEntropy: 1
## nmiss : 0 nmiss : 0
## entropy : 7.48 entropy : 3.8
## normedEntropy: 0.99 normedEntropy: 1.0
summary(dtfile [,-c(1,2,3)])
## ASBM01A ASBM01B ASBM01C ASBM01D
## Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000
## 1st Qu.:1.000 1st Qu.:2.000 1st Qu.:2.000 1st Qu.:1.000
## Median :1.000 Median :4.000 Median :4.000 Median :1.000
## Mean :1.684 Mean :3.371 Mean :3.494 Mean :2.001
## 3rd Qu.:2.000 3rd Qu.:4.000 3rd Qu.:4.000 3rd Qu.:2.000
## Max. :9.000 Max. :9.000 Max. :9.000 Max. :9.000
## NA's :112 NA's :101 NA's :95 NA's :85
## ASBM01E ASBM01F ASBM01G ASBM01H
## Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000
## 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:1.000
## Median :1.000 Median :1.000 Median :1.000 Median :1.000
## Mean :2.004 Mean :2.048 Mean :2.037 Mean :2.142
## 3rd Qu.:2.000 3rd Qu.:2.000 3rd Qu.:2.000 3rd Qu.:2.000
## Max. :9.000 Max. :9.000 Max. :9.000 Max. :9.000
## NA's :74 NA's :69 NA's :68 NA's :68
## ASBM01I ASMMAT03 Gender
## Min. :1.000 Min. : 40.78 Male :2156
## 1st Qu.:1.000 1st Qu.:323.09 Female:2181
## Median :1.000 Median :384.41
## Mean :2.133 Mean :384.26
## 3rd Qu.:3.000 3rd Qu.:446.29
## Max. :9.000 Max. :722.22
## NA's :55
describe(dtfile [,-c(1,2,3)])
## vars n mean sd median trimmed mad min max range
## ASBM01A 1 4225 1.68 1.59 1.00 1.28 0.00 1.00 9.00 8.00
## ASBM01B 2 4236 3.37 1.85 4.00 3.23 0.00 1.00 9.00 8.00
## ASBM01C 3 4242 3.49 1.93 4.00 3.29 0.00 1.00 9.00 8.00
## ASBM01D 4 4252 2.00 2.12 1.00 1.43 0.00 1.00 9.00 8.00
## ASBM01E 5 4263 2.00 2.09 1.00 1.45 0.00 1.00 9.00 8.00
## ASBM01F 6 4268 2.05 2.08 1.00 1.51 0.00 1.00 9.00 8.00
## ASBM01G 7 4269 2.04 2.08 1.00 1.50 0.00 1.00 9.00 8.00
## ASBM01H 8 4269 2.14 2.11 1.00 1.62 0.00 1.00 9.00 8.00
## ASBM01I 9 4282 2.13 2.02 1.00 1.67 0.00 1.00 9.00 8.00
## ASMMAT03 10 4337 384.26 90.28 384.41 384.30 91.31 40.78 722.22 681.44
## Gender* 11 4337 1.50 0.50 2.00 1.50 0.00 1.00 2.00 1.00
## skew kurtosis se
## ASBM01A 3.32 11.80 0.02
## ASBM01B 1.18 2.59 0.03
## ASBM01C 1.22 2.29 0.03
## ASBM01D 2.55 5.52 0.03
## ASBM01E 2.54 5.60 0.03
## ASBM01F 2.55 5.68 0.03
## ASBM01G 2.53 5.62 0.03
## ASBM01H 2.36 4.85 0.03
## ASBM01I 2.35 5.18 0.03
## ASMMAT03 -0.03 -0.12 1.37
## Gender* -0.01 -2.00 0.01
Ploting the Variables
hist(dtfile$ASBM01A)
hist(dtfile$ASBM01B)
hist(dtfile$ASBM01C)
hist(dtfile$ASBM01D)
hist(dtfile$ASBM01E)
hist(dtfile$ASBM01F)
hist(dtfile$ASBM01G)
hist(dtfile$ASBM01H)
hist(dtfile$ASBM01I)
hist(dtfile$ASMMAT03)
Multiple REgression Model
Regression_Model <- lm(ASMMAT03 ~ Gender + IDSCHOOL+ ASBM01A
+ ASBM01B + ASBM01C + ASBM01D + ASBM01E + ASBM01F
+ ASBM01G + ASBM01H + ASBM01I , data = dtfile)
summary(Regression_Model)
##
## Call:
## lm(formula = ASMMAT03 ~ Gender + IDSCHOOL + ASBM01A + ASBM01B +
## ASBM01C + ASBM01D + ASBM01E + ASBM01F + ASBM01G + ASBM01H +
## ASBM01I, data = dtfile)
##
## Residuals:
## Min 1Q Median 3Q Max
## -254.430 -45.244 -0.145 46.625 255.655
##
## Coefficients: (1 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 562.7595 26.3226 21.379 < 2e-16 ***
## GenderFemale -80.8641 29.7901 -2.714 0.006668 **
## IDSCHOOL2 -152.6410 31.7796 -4.803 1.62e-06 ***
## IDSCHOOL3 -239.2549 35.8911 -6.666 3.00e-11 ***
## IDSCHOOL4 -153.2201 38.5798 -3.972 7.27e-05 ***
## IDSCHOOL5 -144.7972 35.9285 -4.030 5.68e-05 ***
## IDSCHOOL6 -320.0644 33.5421 -9.542 < 2e-16 ***
## IDSCHOOL7 -1.1648 20.3316 -0.057 0.954318
## IDSCHOOL8 -83.3419 20.4830 -4.069 4.82e-05 ***
## IDSCHOOL9 -7.4968 20.2829 -0.370 0.711692
## IDSCHOOL10 -190.1840 29.5543 -6.435 1.39e-10 ***
## IDSCHOOL11 -224.4101 28.7439 -7.807 7.50e-15 ***
## IDSCHOOL12 -212.3076 29.6527 -7.160 9.65e-13 ***
## IDSCHOOL13 -192.7788 30.0977 -6.405 1.69e-10 ***
## IDSCHOOL14 24.4415 27.1195 0.901 0.367511
## IDSCHOOL15 -273.1820 32.1227 -8.504 < 2e-16 ***
## IDSCHOOL16 -111.3815 21.6471 -5.145 2.81e-07 ***
## IDSCHOOL17 -62.4803 20.2514 -3.085 0.002048 **
## IDSCHOOL18 -222.8851 31.7993 -7.009 2.82e-12 ***
## IDSCHOOL19 -82.6938 20.0326 -4.128 3.74e-05 ***
## IDSCHOOL20 -115.7667 19.1491 -6.046 1.63e-09 ***
## IDSCHOOL21 -91.8136 19.6503 -4.672 3.08e-06 ***
## IDSCHOOL22 -161.4220 19.1666 -8.422 < 2e-16 ***
## IDSCHOOL23 -26.9157 19.6415 -1.370 0.170658
## IDSCHOOL24 -248.9520 34.9701 -7.119 1.29e-12 ***
## IDSCHOOL25 -269.8955 30.9045 -8.733 < 2e-16 ***
## IDSCHOOL26 -231.0698 29.9749 -7.709 1.61e-14 ***
## IDSCHOOL27 -228.1660 29.0260 -7.861 4.93e-15 ***
## IDSCHOOL28 -171.5002 29.0254 -5.909 3.75e-09 ***
## IDSCHOOL29 -197.6484 29.1348 -6.784 1.35e-11 ***
## IDSCHOOL30 -75.3418 31.7472 -2.373 0.017685 *
## IDSCHOOL31 -13.0635 21.3107 -0.613 0.539912
## IDSCHOOL32 -216.1971 33.5411 -6.446 1.29e-10 ***
## IDSCHOOL33 -214.2032 30.9207 -6.928 5.01e-12 ***
## IDSCHOOL34 -166.6058 31.9037 -5.222 1.86e-07 ***
## IDSCHOOL35 -199.4504 30.7316 -6.490 9.68e-11 ***
## IDSCHOOL36 -36.5725 29.6700 -1.233 0.217785
## IDSCHOOL37 -153.5790 21.6620 -7.090 1.59e-12 ***
## IDSCHOOL38 -122.3763 20.2528 -6.042 1.66e-09 ***
## IDSCHOOL39 -102.8905 19.4655 -5.286 1.32e-07 ***
## IDSCHOOL40 -241.9232 29.1288 -8.305 < 2e-16 ***
## IDSCHOOL41 -170.1083 29.5430 -5.758 9.18e-09 ***
## IDSCHOOL42 -218.8778 29.5348 -7.411 1.54e-13 ***
## IDSCHOOL43 -101.5877 18.1954 -5.583 2.53e-08 ***
## IDSCHOOL44 -110.5227 21.6365 -5.108 3.41e-07 ***
## IDSCHOOL45 -48.9798 20.2640 -2.417 0.015692 *
## IDSCHOOL46 -167.1365 21.0112 -7.955 2.35e-15 ***
## IDSCHOOL47 -24.9385 20.4864 -1.217 0.223558
## IDSCHOOL48 -58.8125 23.3293 -2.521 0.011743 *
## IDSCHOOL49 -69.0061 27.1505 -2.542 0.011073 *
## IDSCHOOL50 -119.2751 20.4804 -5.824 6.23e-09 ***
## IDSCHOOL51 -60.3752 19.8380 -3.043 0.002355 **
## IDSCHOOL52 -91.0184 18.6191 -4.888 1.06e-06 ***
## IDSCHOOL53 -92.6960 18.6255 -4.977 6.75e-07 ***
## IDSCHOOL54 -91.2491 20.1220 -4.535 5.94e-06 ***
## IDSCHOOL55 -178.4365 29.9609 -5.956 2.82e-09 ***
## IDSCHOOL56 -75.2859 31.1678 -2.416 0.015760 *
## IDSCHOOL57 -212.7497 29.0456 -7.325 2.91e-13 ***
## IDSCHOOL58 -244.1387 30.6738 -7.959 2.27e-15 ***
## IDSCHOOL59 -179.8983 29.7873 -6.039 1.69e-09 ***
## IDSCHOOL60 -80.8264 27.1439 -2.978 0.002922 **
## IDSCHOOL61 -212.1523 31.1541 -6.810 1.13e-11 ***
## IDSCHOOL62 -224.3607 32.5389 -6.895 6.27e-12 ***
## IDSCHOOL63 -178.3692 30.4673 -5.854 5.19e-09 ***
## IDSCHOOL64 -77.7178 19.3615 -4.014 6.08e-05 ***
## IDSCHOOL65 -85.7908 20.7642 -4.132 3.68e-05 ***
## IDSCHOOL66 -157.7202 18.8879 -8.350 < 2e-16 ***
## IDSCHOOL67 -187.3668 20.0528 -9.344 < 2e-16 ***
## IDSCHOOL68 -97.6625 30.2934 -3.224 0.001275 **
## IDSCHOOL69 -237.6441 32.1228 -7.398 1.69e-13 ***
## IDSCHOOL70 -189.3653 31.4294 -6.025 1.85e-09 ***
## IDSCHOOL71 -213.3353 32.0990 -6.646 3.44e-11 ***
## IDSCHOOL72 -237.6141 30.9795 -7.670 2.17e-14 ***
## IDSCHOOL73 -103.5832 18.7389 -5.528 3.46e-08 ***
## IDSCHOOL74 -180.4002 31.8181 -5.670 1.54e-08 ***
## IDSCHOOL75 -128.7442 31.1411 -4.134 3.64e-05 ***
## IDSCHOOL76 -195.8587 29.6587 -6.604 4.56e-11 ***
## IDSCHOOL77 -167.9382 30.9331 -5.429 6.02e-08 ***
## IDSCHOOL78 -218.3677 31.4311 -6.947 4.35e-12 ***
## IDSCHOOL79 -121.1916 18.5088 -6.548 6.62e-11 ***
## IDSCHOOL80 -27.3603 28.3310 -0.966 0.334236
## IDSCHOOL81 -33.2937 20.7487 -1.605 0.108662
## IDSCHOOL82 -144.6910 21.6332 -6.688 2.59e-11 ***
## IDSCHOOL83 -94.8394 19.6518 -4.826 1.45e-06 ***
## IDSCHOOL84 -107.9912 17.8779 -6.040 1.68e-09 ***
## IDSCHOOL85 -232.7968 29.7905 -7.814 7.09e-15 ***
## IDSCHOOL86 -89.0222 30.2629 -2.942 0.003285 **
## IDSCHOOL87 -295.9578 29.6661 -9.976 < 2e-16 ***
## IDSCHOOL88 -242.6931 29.1240 -8.333 < 2e-16 ***
## IDSCHOOL89 -297.3691 30.5360 -9.738 < 2e-16 ***
## IDSCHOOL90 -99.4294 20.0527 -4.958 7.42e-07 ***
## IDSCHOOL91 -41.3087 19.6548 -2.102 0.035644 *
## IDSCHOOL92 -103.4714 19.6468 -5.267 1.47e-07 ***
## IDSCHOOL93 -83.8805 21.6472 -3.875 0.000108 ***
## IDSCHOOL94 -90.8921 18.8623 -4.819 1.50e-06 ***
## IDSCHOOL95 -255.7439 30.9057 -8.275 < 2e-16 ***
## IDSCHOOL96 -109.4082 18.5100 -5.911 3.70e-09 ***
## IDSCHOOL97 -134.5168 20.4839 -6.567 5.83e-11 ***
## IDSCHOOL98 -49.5825 18.6027 -2.665 0.007723 **
## IDSCHOOL99 -161.4493 19.4639 -8.295 < 2e-16 ***
## IDSCHOOL100 -39.5154 20.2618 -1.950 0.051221 .
## IDSCHOOL101 -265.6481 29.9325 -8.875 < 2e-16 ***
## IDSCHOOL102 -150.6188 30.9006 -4.874 1.14e-06 ***
## IDSCHOOL103 -201.2527 31.4335 -6.402 1.71e-10 ***
## IDSCHOOL104 -157.9063 29.9329 -5.275 1.40e-07 ***
## IDSCHOOL105 -111.2279 20.7386 -5.363 8.66e-08 ***
## IDSCHOOL106 -63.1663 20.7471 -3.045 0.002346 **
## IDSCHOOL107 -41.3020 20.0431 -2.061 0.039403 *
## IDSCHOOL108 -183.8571 21.6407 -8.496 < 2e-16 ***
## IDSCHOOL109 -99.8319 25.2678 -3.951 7.93e-05 ***
## IDSCHOOL110 -141.4913 21.6517 -6.535 7.21e-11 ***
## IDSCHOOL111 -72.5036 21.0144 -3.450 0.000566 ***
## IDSCHOOL112 -205.8807 31.4537 -6.546 6.72e-11 ***
## IDSCHOOL113 -184.3107 32.5234 -5.667 1.56e-08 ***
## IDSCHOOL114 -254.6444 29.8245 -8.538 < 2e-16 ***
## IDSCHOOL115 -235.8904 29.2068 -8.077 8.85e-16 ***
## IDSCHOOL116 -246.9488 28.4170 -8.690 < 2e-16 ***
## IDSCHOOL117 -279.2137 30.9313 -9.027 < 2e-16 ***
## IDSCHOOL118 -222.8378 29.3208 -7.600 3.71e-14 ***
## IDSCHOOL119 -206.2847 31.4849 -6.552 6.44e-11 ***
## IDSCHOOL120 -205.8994 30.2886 -6.798 1.23e-11 ***
## IDSCHOOL121 -206.3966 43.4907 -4.746 2.15e-06 ***
## IDSCHOOL122 -47.7691 19.4745 -2.453 0.014215 *
## IDSCHOOL123 -42.0809 24.5502 -1.714 0.086596 .
## IDSCHOOL124 -180.2553 32.5117 -5.544 3.15e-08 ***
## IDSCHOOL125 36.6256 26.2351 1.396 0.162781
## IDSCHOOL126 -166.8919 30.6709 -5.441 5.62e-08 ***
## IDSCHOOL127 -142.1368 30.6830 -4.632 3.73e-06 ***
## IDSCHOOL128 -204.4069 30.2871 -6.749 1.71e-11 ***
## IDSCHOOL129 -20.4478 31.4406 -0.650 0.515497
## IDSCHOOL130 -85.9765 20.2651 -4.243 2.26e-05 ***
## IDSCHOOL131 -244.9237 30.7311 -7.970 2.08e-15 ***
## IDSCHOOL132 -131.6692 30.1035 -4.374 1.25e-05 ***
## IDSCHOOL133 -27.4551 29.5752 -0.928 0.353303
## IDSCHOOL134 -230.1703 29.3145 -7.852 5.29e-15 ***
## IDSCHOOL135 -266.9920 29.5617 -9.032 < 2e-16 ***
## IDSCHOOL136 -46.9328 19.0032 -2.470 0.013565 *
## IDSCHOOL137 -178.4686 20.0394 -8.906 < 2e-16 ***
## IDSCHOOL138 -82.4303 18.5040 -4.455 8.64e-06 ***
## IDSCHOOL139 -61.6431 18.7374 -3.290 0.001012 **
## IDSCHOOL140 -133.7644 31.1460 -4.295 1.79e-05 ***
## IDSCHOOL141 -34.3658 20.2764 -1.695 0.090182 .
## IDSCHOOL142 -83.0082 19.4607 -4.265 2.04e-05 ***
## IDSCHOOL143 5.3867 18.7482 0.287 0.773885
## IDSCHOOL144 -91.4986 21.0176 -4.353 1.38e-05 ***
## IDSCHOOL145 -321.8597 30.4167 -10.582 < 2e-16 ***
## IDSCHOOL146 -252.0456 33.5379 -7.515 7.04e-14 ***
## IDSCHOOL147 -156.4201 31.4454 -4.974 6.84e-07 ***
## IDSCHOOL148 -161.4533 30.9026 -5.225 1.84e-07 ***
## IDSCHOOL149 -67.3991 19.8438 -3.396 0.000690 ***
## IDSCHOOL150 -101.2185 21.6670 -4.672 3.09e-06 ***
## IDSCHOOL151 -96.3190 21.0207 -4.582 4.75e-06 ***
## IDSCHOOL152 -161.9275 30.4564 -5.317 1.12e-07 ***
## IDSCHOOL153 -204.9136 34.1972 -5.992 2.26e-09 ***
## IDSCHOOL154 -229.6931 31.1509 -7.374 2.03e-13 ***
## IDSCHOOL155 7.0913 29.8021 0.238 0.811936
## IDSCHOOL156 -77.0973 27.1307 -2.842 0.004511 **
## IDSCHOOL157 -29.1180 23.3547 -1.247 0.212559
## IDSCHOOL158 -152.7382 18.6626 -8.184 3.70e-16 ***
## IDSCHOOL159 -57.6475 19.4803 -2.959 0.003103 **
## IDSCHOOL160 -207.9735 32.5168 -6.396 1.79e-10 ***
## IDSCHOOL161 -218.7214 30.1009 -7.266 4.46e-13 ***
## IDSCHOOL162 -202.6801 29.2050 -6.940 4.59e-12 ***
## IDSCHOOL163 -208.3977 29.5601 -7.050 2.12e-12 ***
## IDSCHOOL164 -212.3900 28.8038 -7.374 2.03e-13 ***
## IDSCHOOL165 -113.3317 19.0134 -5.961 2.74e-09 ***
## IDSCHOOL166 -132.6207 19.0074 -6.977 3.53e-12 ***
## IDSCHOOL167 -113.9466 18.8790 -6.036 1.73e-09 ***
## IDSCHOOL168 20.5817 31.6594 0.650 0.515669
## IDSCHOOL169 -73.4146 29.7949 -2.464 0.013783 *
## IDSCHOOL170 -237.1133 31.5254 -7.521 6.72e-14 ***
## IDSCHOOL171 -227.7551 31.7692 -7.169 9.03e-13 ***
## IDSCHOOL172 -177.3039 29.7854 -5.953 2.88e-09 ***
## IDSCHOOL173 -180.6617 30.6746 -5.890 4.21e-09 ***
## IDSCHOOL174 -113.7495 18.8732 -6.027 1.83e-09 ***
## IDSCHOOL175 -261.4133 33.1102 -7.895 3.76e-15 ***
## IDSCHOOL176 -63.3139 31.7585 -1.994 0.046266 *
## IDSCHOOL177 -195.9926 29.9618 -6.541 6.90e-11 ***
## IDSCHOOL178 -179.5935 30.9172 -5.809 6.80e-09 ***
## IDSCHOOL179 -197.4734 32.5243 -6.072 1.39e-09 ***
## IDSCHOOL180 -56.6853 19.3003 -2.937 0.003334 **
## IDSCHOOL181 -108.5058 19.8363 -5.470 4.79e-08 ***
## IDSCHOOL182 -77.5054 19.8266 -3.909 9.42e-05 ***
## IDSCHOOL183 -147.2850 18.2900 -8.053 1.07e-15 ***
## IDSCHOOL184 -93.1731 22.8623 -4.075 4.69e-05 ***
## IDSCHOOL185 -67.2483 21.3066 -3.156 0.001611 **
## IDSCHOOL186 -26.3091 22.8444 -1.152 0.249531
## IDSCHOOL187 -183.0709 32.9836 -5.550 3.05e-08 ***
## IDSCHOOL188 NA NA NA NA
## IDSCHOOL189 -62.7300 23.3265 -2.689 0.007193 **
## ASBM01A -1.2465 1.0091 -1.235 0.216821
## ASBM01B 5.4427 0.8168 6.663 3.06e-11 ***
## ASBM01C 3.3847 0.7857 4.308 1.69e-05 ***
## ASBM01D -2.0998 0.8208 -2.558 0.010558 *
## ASBM01E -1.3600 1.0210 -1.332 0.182944
## ASBM01F 0.6827 0.9900 0.690 0.490517
## ASBM01G 0.3844 1.1435 0.336 0.736757
## ASBM01H -1.5915 1.1816 -1.347 0.178103
## ASBM01I -6.1758 1.2046 -5.127 3.10e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 69.33 on 3811 degrees of freedom
## (328 observations deleted due to missingness)
## Multiple R-squared: 0.4289, Adjusted R-squared: 0.3994
## F-statistic: 14.53 on 197 and 3811 DF, p-value: < 2.2e-16
histogram(~ ASMMAT03 |ITSEX, data = dtfile)
histogram(~ ASMMAT03 | IDSCHOOL, data = dtfile)
boxplot(ASMMAT03 ~ IDSCHOOL, data = dtfile)
plotSlopes(Regression_Model, plotx = "ASBM01B", modx = "IDSCHOOL")
## Warning in predict.lm(structure(list(coefficients =
## structure(c(562.759500659585, : prediction from a rank-deficient fit may be
## misleading
Base Multilevel Model
first.model <- lmer(ASMMAT03 ~ (1| IDSCHOOL), data = dtfile)
summary(first.model)
## Linear mixed model fit by REML ['lmerMod']
## Formula: ASMMAT03 ~ (1 | IDSCHOOL)
## Data: dtfile
##
## REML criterion at convergence: 49816.8
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.6407 -0.6667 -0.0045 0.6857 3.6889
##
## Random effects:
## Groups Name Variance Std.Dev.
## IDSCHOOL (Intercept) 3340 57.79
## Residual 5071 71.21
## Number of obs: 4337, groups: IDSCHOOL, 189
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 387.661 4.359 88.93
icc(first.model)
##
## Linear mixed model
## Family: gaussian (identity)
## Formula: ASMMAT03 ~ (1 | IDSCHOOL)
##
## ICC (IDSCHOOL): 0.397096
outreg(list("Model1"= first.model), type = "html", browse = FALSE)
##
## browse = FALSE.
## [1] "<table>\n \n"
## [2] "<tr><td> </td><td> Model1</td></tr>\n"
## [3] "<tr><td> </td><td> Estimate </tr>\n"
## [4] "<tr><td style=\"border-bottom: solid thin black; border-collapse:collapse;\"> </td><td style=\"border-bottom: solid thin black; border-collapse:collapse;\"> (S.E.)</tr>\n"
## [5] "<tr><td> 1 </td><td>387.661*** </tr>\n"
## [6] "<tr><td> </td><td> (4.359)</tr>\n"
## [7] "\n"
## [8] "<tr><td>N</td><td> 4337 </tr>\n"
## [9] "<tr><td>RMSE </td><td>71.207 </td></tr>\n"
## [10] ""
## [11] "<tr><td>Random Effects (σ)</td></tr>\n"
## [12] "<tr><td> Residual </td><td> 71.2 </td></tr>\n"
## [13] "<tr><td> IDSCHOOL </td><td> 57.8 </td></tr>\n"
## [14] "<tr style=\"height:5px;\"><td colspan='2' style=\"border-bottom:double thin black;\"> </td></tr>\n"
## [15] "\n"
## [16] "<tr>\n<td colspan=\"2\">* <it>p</it> ≤0.05** <it>p</it> ≤0.01*** <it>p</it> ≤0.001</tr>\n"
## [17] "</table>\n"
### Plottig this model
basemodel <- ranef(first.model, condVar=TRUE)
dotplot(basemodel)
## $IDSCHOOL
ggplot(data = dtfile[as.numeric(dtfile$IDSCHOOL)<=20,], aes(x=IDSCHOOL, y=ASMMAT03)) + geom_point() + facet_wrap(~IDSCHOOL)
ggplot(data = dtfile[as.numeric(dtfile$IDSCHOOL)<=20,], aes(x=IDSCHOOL, y=ASMMAT03)) + geom_boxplot() + facet_wrap(~IDSCHOOL)
Second Model
second.model <- lmer(ASMMAT03 ~ ITSEX + ASBM01A
+ ASBM01B + ASBM01C + ASBM01D + ASBM01E + ASBM01F
+ ASBM01G + ASBM01H + ASBM01I + ( 1| IDSCHOOL), dtfile, REML = FALSE)
summary(second.model)
## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula:
## ASMMAT03 ~ ITSEX + ASBM01A + ASBM01B + ASBM01C + ASBM01D + ASBM01E +
## ASBM01F + ASBM01G + ASBM01H + ASBM01I + (1 | IDSCHOOL)
## Data: dtfile
##
## AIC BIC logLik deviance df.resid
## 45854.1 45936.0 -22914.1 45828.1 3996
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.7476 -0.6684 -0.0062 0.6772 3.6552
##
## Random effects:
## Groups Name Variance Std.Dev.
## IDSCHOOL (Intercept) 2677 51.74
## Residual 4798 69.27
## Number of obs: 4009, groups: IDSCHOOL, 189
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 432.1607 12.8660 33.589
## ITSEX -32.6655 7.9124 -4.128
## ASBM01A -1.0687 1.0047 -1.064
## ASBM01B 5.4329 0.8133 6.680
## ASBM01C 3.3859 0.7825 4.327
## ASBM01D -2.1003 0.8180 -2.567
## ASBM01E -1.5907 1.0172 -1.564
## ASBM01F 0.6748 0.9860 0.684
## ASBM01G 0.3645 1.1395 0.320
## ASBM01H -1.6865 1.1777 -1.432
## ASBM01I -6.1159 1.2006 -5.094
##
## Correlation of Fixed Effects:
## (Intr) ITSEX ASBM01A ASBM01B ASBM01C ASBM01D ASBM01E ASBM01F
## ITSEX -0.932
## ASBM01A -0.040 -0.001
## ASBM01B -0.104 0.025 -0.018
## ASBM01C -0.098 0.018 0.037 -0.467
## ASBM01D 0.012 -0.014 -0.107 -0.080 -0.013
## ASBM01E 0.030 -0.019 -0.157 0.002 -0.089 -0.109
## ASBM01F 0.015 -0.008 -0.042 -0.050 -0.087 -0.119 -0.125
## ASBM01G 0.010 -0.003 -0.114 -0.054 -0.002 -0.070 -0.221 -0.197
## ASBM01H 0.008 -0.012 -0.083 0.002 -0.020 -0.137 -0.154 -0.132
## ASBM01I -0.008 -0.003 -0.067 -0.021 -0.014 -0.085 -0.144 -0.167
## ASBM01G ASBM01H
## ITSEX
## ASBM01A
## ASBM01B
## ASBM01C
## ASBM01D
## ASBM01E
## ASBM01F
## ASBM01G
## ASBM01H -0.219
## ASBM01I -0.215 -0.374
confint(second.model)
## Computing profile confidence intervals ...
## 2.5 % 97.5 %
## .sig01 46.382920 58.0215589
## .sigma 67.741230 70.8501223
## (Intercept) 406.842246 457.5219032
## ITSEX -48.266788 -17.0891826
## ASBM01A -3.038501 0.9014459
## ASBM01B 3.838506 7.0273649
## ASBM01C 1.851740 4.9199857
## ASBM01D -3.703966 -0.4965415
## ASBM01E -3.585668 0.4037699
## ASBM01F -1.258206 2.6076993
## ASBM01G -1.869400 2.5983604
## ASBM01H -3.995614 0.6223680
## ASBM01I -8.469653 -3.7619871
outreg(list("Model2"= second.model), type = "html", browse = FALSE)
##
## browse = FALSE.
## [1] "<table>\n \n"
## [2] "<tr><td> </td><td> Model2</td></tr>\n"
## [3] "<tr><td> </td><td> Estimate </tr>\n"
## [4] "<tr><td style=\"border-bottom: solid thin black; border-collapse:collapse;\"> </td><td style=\"border-bottom: solid thin black; border-collapse:collapse;\"> (S.E.)</tr>\n"
## [5] "<tr><td> (Intercept) </td><td>432.161*** </tr>\n"
## [6] "<tr><td> </td><td> (12.866)</tr>\n"
## [7] "<tr><td> ITSEX </td><td>-32.665*** </tr>\n"
## [8] "<tr><td> </td><td> ( 7.912)</tr>\n"
## [9] "<tr><td> ASBM01A </td><td>-1.069 </tr>\n"
## [10] "<tr><td> </td><td> ( 1.005)</tr>\n"
## [11] "<tr><td> ASBM01B </td><td>5.433*** </tr>\n"
## [12] "<tr><td> </td><td> ( 0.813)</tr>\n"
## [13] "<tr><td> ASBM01C </td><td>3.386*** </tr>\n"
## [14] "<tr><td> </td><td> ( 0.783)</tr>\n"
## [15] "<tr><td> ASBM01D </td><td>-2.100* </tr>\n"
## [16] "<tr><td> </td><td> ( 0.818)</tr>\n"
## [17] "<tr><td> ASBM01E </td><td>-1.591 </tr>\n"
## [18] "<tr><td> </td><td> ( 1.017)</tr>\n"
## [19] "<tr><td> ASBM01F </td><td>0.675 </tr>\n"
## [20] "<tr><td> </td><td> ( 0.986)</tr>\n"
## [21] "<tr><td> ASBM01G </td><td>0.365 </tr>\n"
## [22] "<tr><td> </td><td> ( 1.139)</tr>\n"
## [23] "<tr><td> ASBM01H </td><td>-1.687 </tr>\n"
## [24] "<tr><td> </td><td> ( 1.178)</tr>\n"
## [25] "<tr><td> ASBM01I </td><td>-6.116*** </tr>\n"
## [26] "<tr><td> </td><td> ( 1.201)</tr>\n"
## [27] "\n"
## [28] "<tr><td>N</td><td> 4009 </tr>\n"
## [29] "<tr><td>RMSE </td><td>69.267 </td></tr>\n"
## [30] ""
## [31] ""
## [32] "<tr><td>Random Effects (σ)</td></tr>\n"
## [33] "<tr><td> Residual </td><td> 69.3 </td></tr>\n"
## [34] "<tr><td> IDSCHOOL </td><td> 51.7 </td></tr>\n"
## [35] "<tr style=\"height:5px;\"><td colspan='2' style=\"border-bottom:double thin black;\"> </td></tr>\n"
## [36] "\n"
## [37] "<tr>\n<td colspan=\"2\">* <it>p</it> ≤0.05** <it>p</it> ≤0.01*** <it>p</it> ≤0.001</tr>\n"
## [38] "</table>\n"
Thrid Model
third.model <- lmer(ASMMAT03 ~ ITSEX + ASBM01B + ASBM01C + ASBM01D + ASBM01I + (1|IDSCHOOL), data = dtfile)
summary(third.model)
## Linear mixed model fit by REML ['lmerMod']
## Formula: ASMMAT03 ~ ITSEX + ASBM01B + ASBM01C + ASBM01D + ASBM01I + (1 |
## IDSCHOOL)
## Data: dtfile
##
## REML criterion at convergence: 47222.8
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.6807 -0.6555 -0.0090 0.6742 3.7063
##
## Random effects:
## Groups Name Variance Std.Dev.
## IDSCHOOL (Intercept) 2730 52.25
## Residual 4788 69.20
## Number of obs: 4134, groups: IDSCHOOL, 189
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 432.7624 12.9276 33.476
## ITSEX -33.2709 7.9645 -4.177
## ASBM01B 5.0614 0.7762 6.521
## ASBM01C 3.2700 0.7392 4.424
## ASBM01D -2.9589 0.7302 -4.052
## ASBM01I -7.6560 0.7836 -9.770
##
## Correlation of Fixed Effects:
## (Intr) ITSEX ASBM01B ASBM01C ASBM01D
## ITSEX -0.934
## ASBM01B -0.100 0.023
## ASBM01C -0.091 0.015 -0.474
## ASBM01D 0.022 -0.027 -0.127 -0.073
## ASBM01I 0.016 -0.037 -0.115 -0.136 -0.536
confint(third.model)
## Computing profile confidence intervals ...
## 2.5 % 97.5 %
## .sig01 46.584927 58.205973
## .sigma 67.662592 70.716982
## (Intercept) 407.444768 458.096002
## ITSEX -48.881110 -17.670849
## ASBM01B 3.540553 6.582151
## ASBM01C 1.821297 4.718246
## ASBM01D -4.389887 -1.528503
## ASBM01I -9.192718 -6.121648
outreg(list("Model3"= third.model), type = "html", browse = FALSE)
##
## browse = FALSE.
## [1] "<table>\n \n"
## [2] "<tr><td> </td><td> Model3</td></tr>\n"
## [3] "<tr><td> </td><td> Estimate </tr>\n"
## [4] "<tr><td style=\"border-bottom: solid thin black; border-collapse:collapse;\"> </td><td style=\"border-bottom: solid thin black; border-collapse:collapse;\"> (S.E.)</tr>\n"
## [5] "<tr><td> (Intercept) </td><td>432.762*** </tr>\n"
## [6] "<tr><td> </td><td> (12.928)</tr>\n"
## [7] "<tr><td> ITSEX </td><td>-33.271*** </tr>\n"
## [8] "<tr><td> </td><td> ( 7.964)</tr>\n"
## [9] "<tr><td> ASBM01B </td><td>5.061*** </tr>\n"
## [10] "<tr><td> </td><td> ( 0.776)</tr>\n"
## [11] "<tr><td> ASBM01C </td><td>3.270*** </tr>\n"
## [12] "<tr><td> </td><td> ( 0.739)</tr>\n"
## [13] "<tr><td> ASBM01D </td><td>-2.959*** </tr>\n"
## [14] "<tr><td> </td><td> ( 0.730)</tr>\n"
## [15] "<tr><td> ASBM01I </td><td>-7.656*** </tr>\n"
## [16] "<tr><td> </td><td> ( 0.784)</tr>\n"
## [17] "\n"
## [18] "<tr><td>N</td><td> 4134 </tr>\n"
## [19] "<tr><td>RMSE </td><td>69.196 </td></tr>\n"
## [20] ""
## [21] ""
## [22] "<tr><td>Random Effects (σ)</td></tr>\n"
## [23] "<tr><td> Residual </td><td> 69.2 </td></tr>\n"
## [24] "<tr><td> IDSCHOOL </td><td> 52.2 </td></tr>\n"
## [25] "<tr style=\"height:5px;\"><td colspan='2' style=\"border-bottom:double thin black;\"> </td></tr>\n"
## [26] "\n"
## [27] "<tr>\n<td colspan=\"2\">* <it>p</it> ≤0.05** <it>p</it> ≤0.01*** <it>p</it> ≤0.001</tr>\n"
## [28] "</table>\n"
third.model1<-ranef(third.model, condVar=TRUE)
dotplot(third.model1)
## $IDSCHOOL
