suppressPackageStartupMessages(library(tidyverse))
suppressPackageStartupMessages(library(lme4))stardata <- haven::read_dta("projectSTAR.dta")
glimpse(stardata)## Rows: 6,325
## Columns: 27
## $ stdntid <dbl> 10001, 10133, 10246, 10263, 10266, 10275, 10281, 10282, …
## $ race <dbl+lbl> 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1…
## $ gender <dbl+lbl> 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 2…
## $ FLAGSGK <dbl+lbl> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1…
## $ flaggk <dbl+lbl> 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1…
## $ gkclasstype <dbl+lbl> 3, 3, 3, 1, 2, 3, 1, 3, 1, 2, 3, 3, 2, 3, 3, 3, 1, 2…
## $ gkschid <dbl> 169229, 169280, 218562, 205492, 257899, 161176, 189382, …
## $ gksurban <dbl+lbl> 2, 2, 4, 2, 3, 3, 2, 2, 3, 3, 3, 2, 2, 2, 2, 3, 3, 3…
## $ gktchid <dbl> 16922904, 16928003, 21856202, 20549204, 25789904, 161176…
## $ gktgen <dbl+lbl> 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2…
## $ gktrace <dbl+lbl> 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1…
## $ gkthighdegree <dbl+lbl> 2, 2, 3, 2, 3, 2, 3, 3, 3, 3, 2, 2, 3, 2, 2, 2, 2, 2…
## $ gktcareer <dbl+lbl> 4, 4, 4, 4, 4, NA, 4, 4, 4, 4, 4, 4, 4, …
## $ gktyears <dbl> 5, 7, 8, 3, 12, 2, 7, 14, 4, 6, 11, 16, 12, 5, 17, 10, 6…
## $ gkclasssize <dbl> 24, 22, 17, 17, 24, 24, 13, 24, 14, 23, 23, 22, 20, 24, …
## $ gkfreelunch <dbl+lbl> 2, 2, 2, 1, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2…
## $ gkrepeat <dbl+lbl> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1…
## $ gkspeced <dbl+lbl> 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2…
## $ gkspecin <dbl+lbl> 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2…
## $ gkpresent <dbl> 161, 175, 132, 178, 170, 94, 160, 154, 172, 95, 163, 172…
## $ gkabsent <dbl> 19, 5, 28, 2, 10, 3, 2, 7, 8, 2, 17, 8, 0, 31, 7, NA, 20…
## $ gktreadss <dbl> NA, 427, 450, 483, 456, 411, 443, 448, 463, 472, 428, 54…
## $ gktmathss <dbl> NA, 478, 494, 513, 513, 468, 473, 449, 520, 536, 484, 62…
## $ gktlistss <dbl> NA, 509, 549, 554, 520, 571, 595, 540, 565, 595, NA, 622…
## $ gkwordskillss <dbl> NA, 418, 444, 431, 468, 396, 444, 444, 480, 486, 423, 52…
## $ gkmotivraw <dbl> 23, 24, 28, 27, 25, 24, NA, NA, 26, 27, 24, 24, 23, 28, …
## $ gkselfconcraw <dbl> 52, 53, 56, 61, 54, 55, NA, NA, 52, 61, 55, 49, 49, 59, …str(stardata)## tibble [6,325 × 27] (S3: tbl_df/tbl/data.frame)
## $ stdntid : num [1:6325] 10001 10133 10246 10263 10266 ...
## ..- attr(*, "label")= chr "STUDENT ID"
## ..- attr(*, "format.stata")= chr "%10.0g"
## $ race : dbl+lbl [1:6325] 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1,...
## ..@ label : chr "STUDENT RACE/ETHNICITY"
## ..@ format.stata: chr "%10.0g"
## ..@ labels : Named num [1:6] 1 2 3 4 5 6
## .. ..- attr(*, "names")= chr [1:6] "WHITE" "BLACK" "ASIAN" "HISPANIC" ...
## $ gender : dbl+lbl [1:6325] 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 2,...
## ..@ label : chr "STUDENT GENDER"
## ..@ format.stata: chr "%10.0g"
## ..@ labels : Named num [1:2] 1 2
## .. ..- attr(*, "names")= chr [1:2] "MALE" "FEMALE"
## $ FLAGSGK : dbl+lbl [1:6325] 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,...
## ..@ label : chr "IN STAR IN KINDERGARTEN"
## ..@ format.stata: chr "%10.0g"
## ..@ labels : Named num [1:2] 0 1
## .. ..- attr(*, "names")= chr [1:2] "NO" "YES"
## $ flaggk : dbl+lbl [1:6325] 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1,...
## ..@ label : chr "ACHIEVEMENT DATA AVAILABLE GRADE K"
## ..@ format.stata: chr "%10.0g"
## ..@ labels : Named num [1:2] 0 1
## .. ..- attr(*, "names")= chr [1:2] "NO" "YES"
## $ gkclasstype : dbl+lbl [1:6325] 3, 3, 3, 1, 2, 3, 1, 3, 1, 2, 3, 3, 2, 3, 3, 3, 1, 2,...
## ..@ label : chr "CLASSROOM TYPE KINDERGARTEN"
## ..@ format.stata: chr "%10.0g"
## ..@ labels : Named num [1:3] 1 2 3
## .. ..- attr(*, "names")= chr [1:3] "SMALL CLASS" "REGULAR CLASS" "REGULAR + AIDE CLASS"
## $ gkschid : num [1:6325] 169229 169280 218562 205492 257899 ...
## ..- attr(*, "label")= chr "KINDERGARTEN SCHOOL ID"
## ..- attr(*, "format.stata")= chr "%10.0g"
## $ gksurban : dbl+lbl [1:6325] 2, 2, 4, 2, 3, 3, 2, 2, 3, 3, 3, 2, 2, 2, 2, 3, 3, 3,...
## ..@ label : chr "SCHOOL URBANICITY KINDERGARTEN"
## ..@ format.stata: chr "%10.0g"
## ..@ labels : Named num [1:4] 1 2 3 4
## .. ..- attr(*, "names")= chr [1:4] "INNER CITY" "SUBURBAN" "RURAL" "URBAN"
## $ gktchid : num [1:6325] 16922904 16928003 21856202 20549204 25789904 ...
## ..- attr(*, "label")= chr "KINDERGARTEN TEACHER ID"
## ..- attr(*, "format.stata")= chr "%10.0g"
## $ gktgen : dbl+lbl [1:6325] 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,...
## ..@ label : chr "TEACHER GENDER KINDERGARTEN"
## ..@ format.stata: chr "%10.0g"
## ..@ labels : Named num [1:2] 1 2
## .. ..- attr(*, "names")= chr [1:2] "MALE" "FEMALE"
## $ gktrace : dbl+lbl [1:6325] 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
## ..@ label : chr "TEACHER RACE/ETHNICITY KINDERGARTEN"
## ..@ format.stata: chr "%10.0g"
## ..@ labels : Named num [1:6] 1 2 3 4 5 6
## .. ..- attr(*, "names")= chr [1:6] "WHITE" "BLACK" "ASIAN" "HISPANIC" ...
## $ gkthighdegree: dbl+lbl [1:6325] 2, 2, 3, 2, 3, 2, 3, 3, 3, 3, 2, 2, 3, ...
## ..@ label : chr "TEACHER HIGHEST DEGREE KINDERGARTEN"
## ..@ format.stata: chr "%10.0g"
## ..@ labels : Named num [1:6] 1 2 3 4 5 6
## .. ..- attr(*, "names")= chr [1:6] "ASSOCIATES" "BACHELORS" "MASTERS" "MASTERS +" ...
## $ gktcareer : dbl+lbl [1:6325] 4, 4, 4, 4, 4, NA, 4, 4, 4, 4, 4, 4, 4, ...
## ..@ label : chr "TEACHER CAREER LADDER LEVEL KINDERGARTEN"
## ..@ format.stata: chr "%10.0g"
## ..@ labels : Named num [1:7] 1 2 3 4 5 6 7
## .. ..- attr(*, "names")= chr [1:7] "CHOSE NO TO BE ON CAREER LADDER" "APPRENTICE" "PROBATION" "LADDER LEVEL 1" ...
## $ gktyears : num [1:6325] 5 7 8 3 12 2 7 14 4 6 ...
## ..- attr(*, "label")= chr "YEARS OF TOTAL TEACHING EXPERIENCE KINDERGARTEN"
## ..- attr(*, "format.stata")= chr "%10.0g"
## $ gkclasssize : num [1:6325] 24 22 17 17 24 24 13 24 14 23 ...
## ..- attr(*, "label")= chr "CLASS SIZE KINDERGARTEN"
## ..- attr(*, "format.stata")= chr "%10.0g"
## $ gkfreelunch : dbl+lbl [1:6325] 2, 2, 2, 1, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2,...
## ..@ label : chr "FREE/REDUCED LUNCH STATUS KINDERGARTEN"
## ..@ format.stata: chr "%10.0g"
## ..@ labels : Named num [1:2] 1 2
## .. ..- attr(*, "names")= chr [1:2] "FREE LUNCH" "NON-FREE LUNCH"
## $ gkrepeat : dbl+lbl [1:6325] 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,...
## ..@ label : chr "REPEATING KINDERGARTEN IN 1985-1986 SCHOOL YEAR"
## ..@ format.stata: chr "%10.0g"
## ..@ labels : Named num [1:2] 1 2
## .. ..- attr(*, "names")= chr [1:2] "YES, PROMOTION RECOMMENDED" "NO, PROMOTION NOT RECOMMENDED"
## $ gkspeced : dbl+lbl [1:6325] 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,...
## ..@ label : chr "SPECIAL EDUCATION STATUS KINDERGARTEN"
## ..@ format.stata: chr "%10.0g"
## ..@ labels : Named num [1:2] 1 2
## .. ..- attr(*, "names")= chr [1:2] "YES" "NO"
## $ gkspecin : dbl+lbl [1:6325] 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2,...
## ..@ label : chr "PULLED OUT FOR SPECIAL INSTRUCTION KINDERGARTEN"
## ..@ format.stata: chr "%10.0g"
## ..@ labels : Named num [1:2] 1 2
## .. ..- attr(*, "names")= chr [1:2] "YES" "NO"
## $ gkpresent : num [1:6325] 161 175 132 178 170 94 160 154 172 95 ...
## ..- attr(*, "label")= chr "DAYS PRESENT AT SCHOOL KINDERGARTEN"
## ..- attr(*, "format.stata")= chr "%10.0g"
## $ gkabsent : num [1:6325] 19 5 28 2 10 3 2 7 8 2 ...
## ..- attr(*, "label")= chr "DAYS ABSENT FROM SCHOOL KINDERGARTEN"
## ..- attr(*, "format.stata")= chr "%10.0g"
## $ gktreadss : num [1:6325] NA 427 450 483 456 411 443 448 463 472 ...
## ..- attr(*, "label")= chr "TOTAL READING SCALE SCORE SAT KINDERGARTEN"
## ..- attr(*, "format.stata")= chr "%10.0g"
## $ gktmathss : num [1:6325] NA 478 494 513 513 468 473 449 520 536 ...
## ..- attr(*, "label")= chr "TOTAL MATH SCALE SCORE SAT KINDERGARTEN"
## ..- attr(*, "format.stata")= chr "%10.0g"
## $ gktlistss : num [1:6325] NA 509 549 554 520 571 595 540 565 595 ...
## ..- attr(*, "label")= chr "TOTAL LISTENING SCALE SCORE SAT KINDERGARTEN"
## ..- attr(*, "format.stata")= chr "%10.0g"
## $ gkwordskillss: num [1:6325] NA 418 444 431 468 396 444 444 480 486 ...
## ..- attr(*, "label")= chr "WORD STUDY SKILLS SCALE SCORE SAT KINDERGARTEN"
## ..- attr(*, "format.stata")= chr "%10.0g"
## $ gkmotivraw : num [1:6325] 23 24 28 27 25 24 NA NA 26 27 ...
## ..- attr(*, "label")= chr "MOTIVATION RAW SCORE SCAMIN KINDERGARTEN"
## ..- attr(*, "format.stata")= chr "%10.0g"
## $ gkselfconcraw: num [1:6325] 52 53 56 61 54 55 NA NA 52 61 ...
## ..- attr(*, "label")= chr "SELF-CONCEPT RAW SCORE SCAMIN KINDERGARTEN"
## ..- attr(*, "format.stata")= chr "%10.0g"star.clean <- stardata %>%
mutate (.,
school = gkschid,
class = gktchid,
math = gktmathss,
class_type = as_factor(gkclasstype),
degree = as_factor(gkthighdegree),
self_concept = gkselfconcraw) %>%
group_by(school) %>%
mutate (.,
math_school = mean(gktmathss, na.rm = TRUE)) %>%
ungroup() %>%
select (.,
school,
class,
math,
class_type,
degree,
gkthighdegree,
math_school,
self_concept)
glimpse(star.clean)## Rows: 6,325
## Columns: 8
## $ school <dbl> 169229, 169280, 218562, 205492, 257899, 161176, 189382, …
## $ class <dbl> 16922904, 16928003, 21856202, 20549204, 25789904, 161176…
## $ math <dbl> NA, 478, 494, 513, 513, 468, 473, 449, 520, 536, 484, 62…
## $ class_type <fct> REGULAR + AIDE CLASS, REGULAR + AIDE CLASS, REGULAR + AI…
## $ degree <fct> BACHELORS, BACHELORS, MASTERS, BACHELORS, MASTERS, BACHE…
## $ gkthighdegree <dbl+lbl> 2, 2, 3, 2, 3, 2, 3, 3, 3, 3, 2, 2, 3, 2, 2, 2, 2, 2…
## $ math_school <dbl> 498.8768, 486.9811, 501.1071, 502.6133, 476.2800, 476.78…
## $ self_concept <dbl> 52, 53, 56, 61, 54, 55, NA, NA, 52, 61, 55, 49, 49, 59, …summary(star.clean)## school class math
## Min. :112038 Min. :11203801 Min. :288.0
## 1st Qu.:176329 1st Qu.:17632904 1st Qu.:454.0
## Median :215533 Median :21553306 Median :484.0
## Mean :211227 Mean :21122678 Mean :485.4
## 3rd Qu.:244774 3rd Qu.:24477401 3rd Qu.:513.0
## Max. :264945 Max. :26494505 Max. :626.0
## NA's :454
## class_type degree gkthighdegree math_school
## SMALL CLASS :1900 ASSOCIATES: 0 Min. :2.000 Min. :427.0
## REGULAR CLASS :2194 BACHELORS :4119 1st Qu.:2.000 1st Qu.:474.0
## REGULAR + AIDE CLASS:2231 MASTERS :1981 Median :2.000 Median :486.6
## MASTERS + : 161 Mean :2.386 Mean :485.4
## SPECIALIST: 43 3rd Qu.:3.000 3rd Qu.:502.5
## DOCTORAL : 0 Max. :5.000 Max. :549.6
## NA's : 21 NA's :21
## self_concept
## Min. : 0.00
## 1st Qu.:53.00
## Median :56.00
## Mean :55.95
## 3rd Qu.:59.00
## Max. :72.00
## NA's :1287model.0 <- lmer(math ~ (1|class) + (1|school), REML=FALSE, data=star.clean)
summary(model.0)## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula: math ~ (1 | class) + (1 | school)
## Data: star.clean
##
## AIC BIC logLik deviance df.resid
## 60618.8 60645.5 -30305.4 60610.8 5867
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -6.2037 -0.6273 -0.0635 0.5846 3.9171
##
## Random effects:
## Groups Name Variance Std.Dev.
## class (Intercept) 287.6 16.96
## school (Intercept) 375.8 19.39
## Residual 1612.4 40.15
## Number of obs: 5871, groups: class, 325; school, 79
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 486.00 2.45 198.4##Calculate ICCs
ICC.class = 287.6/(287.6+375.8+1612.4)
ICC.class## [1] 0.126373112.64% of the variability in math scores is between classrooms/teachers within the same school.
ICC.school = 376.8/(287.6+375.8+1612.4)
ICC.school## [1] 0.165568216.56% of the variability in math scores is between schools.
##% variability at student-level
1-(ICC.class+ICC.school)## [1] 0.7080587##Conditional Models##
#Adding L1 Predictor(s)
model.1 <- lmer(math ~ self_concept + (1|class) + (1|school), REML=FALSE, data=star.clean)
summary(model.1)## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula: math ~ self_concept + (1 | class) + (1 | school)
## Data: star.clean
##
## AIC BIC logLik deviance df.resid
## 48969.7 49002.0 -24479.9 48959.7 4751
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.8498 -0.6473 -0.0640 0.5925 3.9068
##
## Random effects:
## Groups Name Variance Std.Dev.
## class (Intercept) 283.8 16.85
## school (Intercept) 395.7 19.89
## Residual 1551.1 39.38
## Number of obs: 4756, groups: class, 301; school, 73
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 461.8349 7.1431 64.655
## self_concept 0.4523 0.1188 3.807
##
## Correlation of Fixed Effects:
## (Intr)
## self_concpt -0.931Estimated math scores for students w/ average self-concept scores = 461.83. Estimated math scores for students increase by 0.45 for each increase in self-concept score.
lmerTest::rand(model.1)## ANOVA-like table for random-effects: Single term deletions
##
## Model:
## math ~ self_concept + (1 | class) + (1 | school)
## npar logLik AIC LRT Df Pr(>Chisq)
## <none> 5 -24480 48970
## (1 | class) 4 -24622 49253 284.956 1 < 2.2e-16 ***
## (1 | school) 4 -24525 49059 90.916 1 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#Adding L2 Predictor(s)
model.2 <- lmer(math ~ self_concept + class_type + degree + (1|class) + (1|school), REML=FALSE, data=star.clean)
summary(model.2)## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula: math ~ self_concept + class_type + degree + (1 | class) + (1 |
## school)
## Data: star.clean
##
## AIC BIC logLik deviance df.resid
## 48961.2 49025.9 -24470.6 48941.2 4746
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.8266 -0.6442 -0.0610 0.5904 3.9341
##
## Random effects:
## Groups Name Variance Std.Dev.
## class (Intercept) 252.1 15.88
## school (Intercept) 407.1 20.18
## Residual 1551.2 39.39
## Number of obs: 4756, groups: class, 301; school, 73
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 467.9764 7.3642 63.547
## self_concept 0.4363 0.1187 3.675
## class_typeREGULAR CLASS -8.1748 2.7014 -3.026
## class_typeREGULAR + AIDE CLASS -8.8767 2.6938 -3.295
## degreeMASTERS 0.1572 2.7666 0.057
## degreeMASTERS + -5.2330 7.5361 -0.694
## degreeSPECIALIST 22.2608 13.2338 1.682
##
## Correlation of Fixed Effects:
## (Intr) slf_cn c_REGC c_R+AC dMASTE dMAST+
## self_concpt -0.906
## c_REGULARCL -0.190 0.030
## c_REGULA+AC -0.188 0.026 0.475
## degrMASTERS -0.090 -0.018 -0.079 -0.075
## dgrMASTERS+ -0.026 -0.012 -0.032 0.001 0.131
## dSPECIALIST -0.040 -0.019 0.119 0.118 0.099 0.015Intercept = predicted math score for a student w/ average self-concept, in a small class, and whose teacher has a Bachelor’s degree. Self-Concept = predicted math score increases by 0.44 for each increase in self-concept Regular Class = predicted math scores for students in a regular class are expected to be about 8.17 points lower than students’ scores in a small class. Regular + Aide Class = predicted math scores for students in a regular/aide class are expected to be about 8.88 points lower than students’ scores in a small class. Degree - Masters = predicted math scores for students whose teacher has a Master’s degree is expected to be about 0.16 points higher compared to students whose teacher has a Bachelor’s degree. not statistically significant difference though. Degree - Masters Plus = predicted math scores for students whose teacher has a Master’s degree + is expected to be about 5.23 points lower than students whose teacher has a Bachelor’s degree. not statistically significant difference Degree - Specialist = predicted math scores for students whose teacher has a Specialist degree are expected to be about 22.26 points higher compared to students whose teacher has a Bachelor’s degree. not statistically significant difference.
anova(model.1, model.2)## Data: star.clean
## Models:
## model.1: math ~ self_concept + (1 | class) + (1 | school)
## model.2: math ~ self_concept + class_type + degree + (1 | class) + (1 | school)
## npar AIC BIC logLik deviance Chisq Df Pr(>Chisq)
## model.1 5 48970 49002 -24480 48960
## model.2 10 48961 49026 -24471 48941 18.484 5 0.002397 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#Adding L3 Predictor(s)
model.3 <- lmer(math ~ self_concept + class_type + degree + math_school + (1|class) + (1|school), REML=FALSE, data=star.clean)## boundary (singular) fit: see help('isSingular')summary(model.3)## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula: math ~ self_concept + class_type + degree + math_school + (1 |
## class) + (1 | school)
## Data: star.clean
##
## AIC BIC logLik deviance df.resid
## 48768.2 48839.3 -24373.1 48746.2 4745
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.7976 -0.6435 -0.0603 0.5904 4.0060
##
## Random effects:
## Groups Name Variance Std.Dev.
## class (Intercept) 174.4 13.21
## school (Intercept) 0.0 0.00
## Residual 1552.8 39.41
## Number of obs: 4756, groups: class, 301; school, 73
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) -14.15268 22.09078 -0.641
## self_concept 0.43544 0.11725 3.714
## class_typeREGULAR CLASS -8.20633 2.35152 -3.490
## class_typeREGULAR + AIDE CLASS -8.69961 2.35099 -3.700
## degreeMASTERS -0.33621 2.10936 -0.159
## degreeMASTERS + -2.37697 5.96377 -0.399
## degreeSPECIALIST 19.25123 10.64910 1.808
## math_school 0.99386 0.04374 22.724
##
## Correlation of Fixed Effects:
## (Intr) slf_cn c_REGC c_R+AC dMASTE dMAST+ dSPECI
## self_concpt -0.274
## c_REGULARCL -0.039 0.030
## c_REGULA+AC -0.059 0.027 0.479
## degrMASTERS 0.019 -0.011 -0.072 -0.064
## dgrMASTERS+ 0.021 -0.007 -0.021 0.000 0.114
## dSPECIALIST 0.003 -0.008 0.101 0.101 0.054 0.021
## math_school -0.951 -0.025 -0.019 0.002 -0.043 -0.030 -0.014
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')help('isSingular')## starting httpd help server ... doneanova(model.2, model.3)## Data: star.clean
## Models:
## model.2: math ~ self_concept + class_type + degree + (1 | class) + (1 | school)
## model.3: math ~ self_concept + class_type + degree + math_school + (1 | class) + (1 | school)
## npar AIC BIC logLik deviance Chisq Df Pr(>Chisq)
## model.2 10 48961 49026 -24471 48941
## model.3 11 48768 48839 -24373 48746 195.05 1 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1model.3b <- lmer(math ~ self_concept + class_type + math_school + (1|class) + (1|school), REML=FALSE, data=star.clean)## boundary (singular) fit: see help('isSingular')summary(model.3b)## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula: math ~ self_concept + class_type + math_school + (1 | class) +
## (1 | school)
## Data: star.clean
##
## AIC BIC logLik deviance df.resid
## 48765.7 48817.4 -24374.8 48749.7 4748
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.7976 -0.6432 -0.0614 0.5883 3.9996
##
## Random effects:
## Groups Name Variance Std.Dev.
## class (Intercept) 177 13.31
## school (Intercept) 0 0.00
## Residual 1553 39.41
## Number of obs: 4756, groups: class, 301; school, 73
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) -14.00052 22.18399 -0.631
## self_concept 0.43628 0.11728 3.720
## class_typeREGULAR CLASS -8.69083 2.34328 -3.709
## class_typeREGULAR + AIDE CLASS -9.16379 2.34436 -3.909
## math_school 0.99406 0.04389 22.647
##
## Correlation of Fixed Effects:
## (Intr) slf_cn c_REGC c_R+AC
## self_concpt -0.273
## c_REGULARCL -0.038 0.030
## c_REGULA+AC -0.058 0.027 0.471
## math_school -0.952 -0.026 -0.022 0.001
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')model.3c <- lmer(math ~ math_school + (1|class) + (1|school), REML=FALSE, data=star.clean)## boundary (singular) fit: see help('isSingular')summary(model.3c)## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula: math ~ math_school + (1 | class) + (1 | school)
## Data: star.clean
##
## AIC BIC logLik deviance df.resid
## 60405.4 60438.8 -30197.7 60395.4 5866
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -6.0261 -0.6306 -0.0617 0.5793 3.9863
##
## Random effects:
## Groups Name Variance Std.Dev.
## class (Intercept) 193.7 13.92
## school (Intercept) 0.0 0.00
## Residual 1613.2 40.16
## Number of obs: 5871, groups: class, 325; school, 79
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 0.84334 21.16579 0.04
## math_school 0.99926 0.04356 22.94
##
## Correlation of Fixed Effects:
## (Intr)
## math_school -0.999
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')library(modelsummary)
library(broom.mixed)
models <- list(model.0, model.1, model.2, model.3)
modelsummary(models, output = "default")| Model 1 | Model 2 | Model 3 | Model 4 | |
|---|---|---|---|---|
| (Intercept) | 486.000 | 461.835 | 467.976 | −14.153 |
| (2.450) | (7.143) | (7.364) | (22.091) | |
| self_concept | 0.452 | 0.436 | 0.435 | |
| (0.119) | (0.119) | (0.117) | ||
| class_typeREGULAR CLASS | −8.175 | −8.206 | ||
| (2.701) | (2.352) | |||
| class_typeREGULAR + AIDE CLASS | −8.877 | −8.700 | ||
| (2.694) | (2.351) | |||
| degreeMASTERS | 0.157 | −0.336 | ||
| (2.767) | (2.109) | |||
| degreeMASTERS + | −5.233 | −2.377 | ||
| (7.536) | (5.964) | |||
| degreeSPECIALIST | 22.261 | 19.251 | ||
| (13.234) | (10.649) | |||
| math_school | 0.994 | |||
| (0.044) | ||||
| SD (Intercept class) | 16.958 | 16.846 | 15.877 | 13.205 |
| SD (Intercept school) | 19.386 | 19.893 | 20.176 | 0.000 |
| SD (Observations) | 40.155 | 39.383 | 39.386 | 39.405 |
| Num.Obs. | 5871 | 4756 | 4756 | 4756 |
| R2 Marg. | 0.000 | 0.002 | 0.012 | 0.249 |
| R2 Cond. | 0.292 | 0.306 | 0.307 | |
| AIC | 60615.1 | 48968.4 | 48935.8 | 48751.2 |
| BIC | 60641.9 | 49000.7 | 49000.5 | 48822.3 |
| ICC | 0.3 | 0.3 | 0.3 | |
| RMSE | 39.25 | 38.39 | 38.42 | 38.61 |
##Adding random slope for self-concept at both teacher and school levels
model_s_slp <- lmer(math ~ self_concept + class_type + degree + math_school + (self_concept|class) + (1|school), REML = FALSE, data = star.clean)## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge with max|grad| = 2.477 (tol = 0.002, component 1)## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: very large eigenvalue
## - Rescale variables?;Model is nearly unidentifiable: large eigenvalue ratio
## - Rescale variables?summary(model_s_slp)## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula:
## math ~ self_concept + class_type + degree + math_school + (self_concept |
## class) + (1 | school)
## Data: star.clean
##
## AIC BIC logLik deviance df.resid
## 48765.4 48849.5 -24369.7 48739.4 4743
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.7930 -0.6469 -0.0626 0.5848 4.0115
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## class (Intercept) 1.342e+03 36.63578
## self_concept 3.791e-01 0.61574 -0.93
## school (Intercept) 8.481e-04 0.02912
## Residual 1.543e+03 39.28519
## Number of obs: 4756, groups: class, 301; school, 73
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) -14.03258 22.06256 -0.636
## self_concept 0.43401 0.12478 3.478
## class_typeREGULAR CLASS -8.17998 2.33708 -3.500
## class_typeREGULAR + AIDE CLASS -8.67689 2.33564 -3.715
## degreeMASTERS -0.34328 2.09511 -0.164
## degreeMASTERS + -2.21733 5.92967 -0.374
## degreeSPECIALIST 19.37670 10.60322 1.827
## math_school 0.99382 0.04346 22.866
##
## Correlation of Fixed Effects:
## (Intr) slf_cn c_REGC c_R+AC dMASTE dMAST+ dSPECI
## self_concpt -0.291
## c_REGULARCL -0.040 0.031
## c_REGULA+AC -0.060 0.028 0.480
## degrMASTERS 0.019 -0.009 -0.072 -0.064
## dgrMASTERS+ 0.020 -0.006 -0.022 -0.001 0.114
## dSPECIALIST 0.003 -0.008 0.101 0.101 0.053 0.021
## math_school -0.945 -0.029 -0.019 0.002 -0.044 -0.029 -0.014
## optimizer (nloptwrap) convergence code: 0 (OK)
## Model failed to converge with max|grad| = 2.477 (tol = 0.002, component 1)
## Model is nearly unidentifiable: very large eigenvalue
## - Rescale variables?
## Model is nearly unidentifiable: large eigenvalue ratio
## - Rescale variables?lmerTest::rand(model_s_slp)## boundary (singular) fit: see help('isSingular')## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge with max|grad| = 9.72245 (tol = 0.002, component 1)## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: very large eigenvalue
## - Rescale variables?## ANOVA-like table for random-effects: Single term deletions
##
## Model:
## math ~ self_concept + class_type + degree + math_school + (self_concept | class) + (1 | school)
## npar logLik AIC LRT Df Pr(>Chisq)
## <none> 13 -24370 48765
## self_concept in (self_concept | class) 11 -24373 48768 6.7463 2 0.03428
## (1 | school) 12 -24369 48763 -0.6240 1 1.00000
##
## <none>
## self_concept in (self_concept | class) *
## (1 | school)
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1models2 <- list(model.3, model_s_slp)
modelsummary(models2, output = "default")| Model 1 | Model 2 | |
|---|---|---|
| (Intercept) | −14.153 | −14.033 |
| (22.091) | (22.063) | |
| self_concept | 0.435 | 0.434 |
| (0.117) | (0.125) | |
| class_typeREGULAR CLASS | −8.206 | −8.180 |
| (2.352) | (2.337) | |
| class_typeREGULAR + AIDE CLASS | −8.700 | −8.677 |
| (2.351) | (2.336) | |
| degreeMASTERS | −0.336 | −0.343 |
| (2.109) | (2.095) | |
| degreeMASTERS + | −2.377 | −2.217 |
| (5.964) | (5.930) | |
| degreeSPECIALIST | 19.251 | 19.377 |
| (10.649) | (10.603) | |
| math_school | 0.994 | 0.994 |
| (0.044) | (0.043) | |
| SD (Intercept class) | 13.205 | 36.636 |
| SD (self_concept class) | 0.616 | |
| Cor (Intercept~self_concept class) | −0.935 | |
| SD (Intercept school) | 0.000 | 0.029 |
| SD (Observations) | 39.405 | 39.285 |
| Num.Obs. | 4756 | 4756 |
| R2 Marg. | 0.249 | 0.230 |
| R2 Cond. | 0.310 | |
| AIC | 48751.2 | 48748.4 |
| BIC | 48822.3 | 48832.5 |
| ICC | 0.1 | |
| RMSE | 38.61 | 38.38 |
model_t_slp <- lmer(math ~ self_concept + class_type + degree + math_school + (1|class) + (self_concept|school), REML = FALSE, data = star.clean)## boundary (singular) fit: see help('isSingular')summary(model_t_slp)## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula: math ~ self_concept + class_type + degree + math_school + (1 |
## class) + (self_concept | school)
## Data: star.clean
##
## AIC BIC logLik deviance df.resid
## 48763.3 48847.4 -24368.7 48737.3 4743
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.7525 -0.6472 -0.0606 0.5866 4.0302
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## class (Intercept) 174.7269 13.2184
## school (Intercept) 1553.6793 39.4167
## self_concept 0.4985 0.7061 -1.00
## Residual 1539.9019 39.2416
## Number of obs: 4756, groups: class, 301; school, 73
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) -14.26371 22.62614 -0.630
## self_concept 0.41592 0.14666 2.836
## class_typeREGULAR CLASS -8.26948 2.35719 -3.508
## class_typeREGULAR + AIDE CLASS -8.67333 2.35483 -3.683
## degreeMASTERS -0.57631 2.11236 -0.273
## degreeMASTERS + -2.53788 5.97827 -0.425
## degreeSPECIALIST 19.53815 10.67695 1.830
## math_school 0.99664 0.04377 22.769
##
## Correlation of Fixed Effects:
## (Intr) slf_cn c_REGC c_R+AC dMASTE dMAST+ dSPECI
## self_concpt -0.342
## c_REGULARCL -0.039 0.027
## c_REGULA+AC -0.058 0.023 0.480
## degrMASTERS 0.019 -0.011 -0.072 -0.064
## dgrMASTERS+ 0.020 -0.005 -0.021 -0.001 0.114
## dSPECIALIST 0.004 -0.010 0.100 0.101 0.052 0.021
## math_school -0.928 -0.023 -0.019 0.002 -0.043 -0.030 -0.014
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')lmerTest::rand(model_t_slp)## boundary (singular) fit: see help('isSingular')
## boundary (singular) fit: see help('isSingular')## ANOVA-like table for random-effects: Single term deletions
##
## Model:
## math ~ self_concept + class_type + degree + math_school + (1 | class) + (self_concept | school)
## npar logLik AIC LRT Df Pr(>Chisq)
## <none> 13 -24369 48763
## (1 | class) 12 -24458 48940 179.122 1 < 2e-16
## self_concept in (self_concept | school) 11 -24373 48768 8.831 2 0.01209
##
## <none>
## (1 | class) ***
## self_concept in (self_concept | school) *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1models3 <- list(model.3, model_t_slp)
modelsummary(models3, output = "default")| Model 1 | Model 2 | |
|---|---|---|
| (Intercept) | −14.153 | −14.264 |
| (22.091) | (22.626) | |
| self_concept | 0.435 | 0.416 |
| (0.117) | (0.147) | |
| class_typeREGULAR CLASS | −8.206 | −8.269 |
| (2.352) | (2.357) | |
| class_typeREGULAR + AIDE CLASS | −8.700 | −8.673 |
| (2.351) | (2.355) | |
| degreeMASTERS | −0.336 | −0.576 |
| (2.109) | (2.112) | |
| degreeMASTERS + | −2.377 | −2.538 |
| (5.964) | (5.978) | |
| degreeSPECIALIST | 19.251 | 19.538 |
| (10.649) | (10.677) | |
| math_school | 0.994 | 0.997 |
| (0.044) | (0.044) | |
| SD (Intercept class) | 13.205 | 13.218 |
| SD (Intercept school) | 0.000 | 39.417 |
| SD (self_concept school) | 0.706 | |
| Cor (Intercept~self_concept school) | −1.000 | |
| SD (Observations) | 39.405 | 39.242 |
| Num.Obs. | 4756 | 4756 |
| R2 Marg. | 0.249 | 0.251 |
| R2 Cond. | ||
| AIC | 48751.2 | 48745.9 |
| BIC | 48822.3 | 48829.9 |
| RMSE | 38.61 | 38.36 |