This is an R Markdown Notebook. When you execute code within the notebook, the results appear beneath the code.

Try executing this chunk by clicking the Run button within the chunk or by placing your cursor inside it and pressing Cmd+Shift+Enter.

Add a new chunk by clicking the Insert Chunk button on the toolbar or by pressing Cmd+Option+I.

When you save the notebook, an HTML file containing the code and output will be saved alongside it (click the Preview button or press Cmd+Shift+K to preview the HTML file).

#Load packages

library(haven)
library(tidyverse)
library(lme4)
library(lmerTest)

#load dataset

projectSTAR <- haven::read_dta("projectSTAR.dta")
glimpse(projectSTAR)
Rows: 6,325
Columns: 27
$ stdntid       <dbl> 10001, 10133, 10246, 10263, 10266, 10275, 10281, 10282, 10285, 10286, 10287, 1028…
$ race          <dbl+lbl> 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1,…
$ gender        <dbl+lbl> 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1,…
$ FLAGSGK       <dbl+lbl> 1, 1, 1, 1, 1, 1, 1, 1, 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, 1, 1, 1, 0, 1, 1, 1, 1,…
$ gkclasstype   <dbl+lbl> 3, 3, 3, 1, 2, 3, 1, 3, 1, 2, 3, 3, 2, 3, 3, 3, 1, 2, 3, 3, 2, 1, 1, 3, 2, 1,…
$ gkschid       <dbl> 169229, 169280, 218562, 205492, 257899, 161176, 189382, 189382, 201449, 230612, 1…
$ gksurban      <dbl+lbl> 2, 2, 4, 2, 3, 3, 2, 2, 3, 3, 3, 2, 2, 2, 2, 3, 3, 3, 3, 3, 2, 1, 2, 3, 1, 4,…
$ gktchid       <dbl> 16922904, 16928003, 21856202, 20549204, 25789904, 16117602, 18938204, 18938203, 2…
$ gktgen        <dbl+lbl> 2, 2, 2, 2, 2, 2, 2, 2, 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,  1,  …
$ gkthighdegree <dbl+lbl>  2,  2,  3,  2,  3,  2,  3,  3,  3,  3,  2,  2,  3,  2,  2,  2,  2,  2,  2,  …
$ gktcareer     <dbl+lbl>  4,  4,  4,  4,  4, NA,  4,  4,  4,  4,  4,  4,  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, 10, 13, 9, 18, 1, 7, 13…
$ gkclasssize   <dbl> 24, 22, 17, 17, 24, 24, 13, 24, 14, 23, 23, 22, 20, 24, 23, 27, 17, 24, 22, 23, 2…
$ gkfreelunch   <dbl+lbl> 2, 2, 2, 1, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 1,…
$ gkrepeat      <dbl+lbl> 1, 1, 1, 1, 1, 1, 1, 1, 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, 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, 2, 2, 2, 2, 2, 1, 2, 2,…
$ gkpresent     <dbl> 161, 175, 132, 178, 170, 94, 160, 154, 172, 95, 163, 172, 180, 149, 173, NA, 160,…
$ gkabsent      <dbl> 19, 5, 28, 2, 10, 3, 2, 7, 8, 2, 17, 8, 0, 31, 7, NA, 20, 7, 2, 19, 24, 0, 8, 9, …
$ gktreadss     <dbl> NA, 427, 450, 483, 456, 411, 443, 448, 463, 472, 428, 545, 408, 422, 472, NA, 437…
$ gktmathss     <dbl> NA, 478, 494, 513, 513, 468, 473, 449, 520, 536, 484, 626, 454, 439, 528, NA, 463…
$ gktlistss     <dbl> NA, 509, 549, 554, 520, 571, 595, 540, 565, 595, NA, 622, 474, 536, 578, NA, 554,…
$ gkwordskillss <dbl> NA, 418, 444, 431, 468, 396, 444, 444, 480, 486, 423, 524, 410, 423, 458, NA, 427…
$ gkmotivraw    <dbl> 23, 24, 28, 27, 25, 24, NA, NA, 26, 27, 24, 24, 23, 28, 24, NA, 26, 25, NA, 26, 2…
$ gkselfconcraw <dbl> 52, 53, 56, 61, 54, 55, NA, NA, 52, 61, 55, 49, 49, 59, 50, NA, 58, 45, NA, 55, 5…

#figure out coding scheme & variables

str(projectSTAR)
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, 1, 1, 1, 2, 1, 1, 2, 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, 2, 2, 1, 1, 1, 1, 1, 1, 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, 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, 1, 1, 1, 0, 1, 1, 1, 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, 3, 3, 2, 1, 1, 3, 2, 1, 1...
   ..@ 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, 3, 3, 2, 1, 2, 3, 1, 4, 2...
   ..@ 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, 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,  2,  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,  2,  2,  2,  2,  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,  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, 2, 1, 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, 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, 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, 2, 2, 2, 2, 2, 1, 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"

#time to clean up these names to be easier to work with & make new dataset ##math scores (gktmathss), self-concept (gkselfconcraw), classroom type (gkclasstype) and teacher highest degree (gkthighdegree), and school average math scores.

star.clean <- projectSTAR %>%
  mutate(.,
         schoolid = gkschid,
         classid = gktchid,
         math = gktmathss,
         classtype = as_factor(gkclasstype),
         years.exp = gktyears,
         degree = as_factor(gkthighdegree),
         selfconcept = gkselfconcraw
         ) %>%
  group_by(schoolid) %>% 
  mutate(.,
            schoolmath = mean(gktmathss, na.rm = TRUE) #average math score via school
  ) %>%
  ungroup() %>%
   select(.,
         schoolid,
         classid,
         math,
         classtype,
         years.exp,
         degree,
         selfconcept,
         schoolmath)
glimpse(star.clean)
Rows: 6,325
Columns: 8
$ schoolid    <dbl> 169229, 169280, 218562, 205492, 257899, 161176, 189382, 189382, 201449, 230612, 128…
$ classid     <dbl> 16922904, 16928003, 21856202, 20549204, 25789904, 16117602, 18938204, 18938203, 201…
$ math        <dbl> NA, 478, 494, 513, 513, 468, 473, 449, 520, 536, 484, 626, 454, 439, 528, NA, 463, …
$ classtype   <fct> REGULAR + AIDE CLASS, REGULAR + AIDE CLASS, REGULAR + AIDE CLASS, SMALL CLASS, REGU…
$ years.exp   <dbl> 5, 7, 8, 3, 12, 2, 7, 14, 4, 6, 11, 16, 12, 5, 17, 10, 6, 10, 13, 9, 18, 1, 7, 13, …
$ degree      <fct> BACHELORS, BACHELORS, MASTERS, BACHELORS, MASTERS, BACHELORS, MASTERS, MASTERS, MAS…
$ selfconcept <dbl> 52, 53, 56, 61, 54, 55, NA, NA, 52, 61, 55, 49, 49, 59, 50, NA, 58, 45, NA, 55, 52,…
$ schoolmath  <dbl> 498.8768, 486.9811, 501.1071, 502.6133, 476.2800, 476.7821, 479.4062, 479.4062, 503…

###Run a null model. DV: gktmathss students clustered within classrooms and schools.

model.null <- lmer(math ~ (1|schoolid) + (1|classid), data = star.clean)
summary(model.null)
Linear mixed model fit by REML. t-tests use Satterthwaite's method ['lmerModLmerTest']
Formula: math ~ (1 | schoolid) + (1 | classid)
   Data: star.clean

REML criterion at convergence: 60607.1

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-6.2037 -0.6274 -0.0630  0.5841  3.9174 

Random effects:
 Groups   Name        Variance Std.Dev.
 classid  (Intercept)  287.6   16.96   
 schoolid (Intercept)  381.9   19.54   
 Residual             1612.4   40.15   
Number of obs: 5871, groups:  classid, 325; schoolid, 79

Fixed effects:
            Estimate Std. Error      df t value Pr(>|t|)    
(Intercept)  486.000      2.466  77.323   197.1   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

#what does degree look like? (We already know what class type looks like) but for practice. Next time run this before null model so I know what I am looking for/at.

table(star.clean$degree)

ASSOCIATES  BACHELORS    MASTERS  MASTERS + SPECIALIST   DOCTORAL 
         0       4119       1981        161         43          0 
table(star.clean$classtype)

         SMALL CLASS        REGULAR CLASS REGULAR + AIDE CLASS 
                1900                 2194                 2231

#Run ICC for class id

ICC.class <- 287.6/(287.6 + 381.9 +1612.4)
ICC.class
[1] 0.1260353

#Run ICC for schoolid

ICC.school <- 381.9/(287.6 + 381.9 + 1612.4)
ICC.school
[1] 0.1673605

#Now, run a conditional random intercept model with math scores (math) as the DV, and self-concept (selfconcept) as a student-level IV.

model.1 <- lmer(math ~ selfconcept + (1| schoolid) + (1|classid), data = star.clean)
summary(model.1)
Linear mixed model fit by REML. t-tests use Satterthwaite's method ['lmerModLmerTest']
Formula: math ~ selfconcept + (1 | schoolid) + (1 | classid)
   Data: star.clean

REML criterion at convergence: 48958.4

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-3.8495 -0.6475 -0.0641  0.5928  3.9066 

Random effects:
 Groups   Name        Variance Std.Dev.
 classid  (Intercept)  283.8   16.85   
 schoolid (Intercept)  402.7   20.07   
 Residual             1551.4   39.39   
Number of obs: 4756, groups:  classid, 301; schoolid, 73

Fixed effects:
             Estimate Std. Error        df t value Pr(>|t|)    
(Intercept)  461.8411     7.1505 2370.9421  64.589  < 2e-16 ***
selfconcept    0.4522     0.1188 4687.5612   3.806 0.000143 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation of Fixed Effects:
            (Intr)
selfconcept -0.930

##Now, run a conditional random intercept model with math scores (math) as the DV, and self-concept (selfconcept) as a student-level IV, classroom type (classtype) and teacher highest degree (degree) as teacher-level IVs.

model.2 <- lmer(math~selfconcept + classtype + degree + (1|classid) + (1|schoolid), REML=FALSE, data=star.clean)
summary(model.2)

Now, run a conditional random intercept model with math scores (math) as the DV, and self-concept (selfconcept) as a student-level IV, classroom type (classtype) and teacher highest degree (degree) as teacher-level IVs, and school average math scores as a school level IV.

model.3 <- lmer(math~selfconcept + classtype + degree + schoolmath + (1|classid) + (1|schoolid), REML=FALSE, data=star.clean)
boundary (singular) fit: see ?isSingular
summary(model.3)
Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's method ['lmerModLmerTest']
Formula: math ~ selfconcept + classtype + degree + schoolmath + (1 | classid) +      (1 | schoolid)
   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.
 classid  (Intercept)  174.4   13.21   
 schoolid (Intercept)    0.0    0.00   
 Residual             1552.8   39.41   
Number of obs: 4756, groups:  classid, 301; schoolid, 73

Fixed effects:
                                Estimate Std. Error         df t value Pr(>|t|)    
(Intercept)                    -14.15268   22.09078  317.69097  -0.641 0.522205    
selfconcept                      0.43544    0.11725 4755.84428   3.714 0.000206 ***
classtypeREGULAR CLASS          -8.20633    2.35152  293.16090  -3.490 0.000558 ***
classtypeREGULAR + AIDE CLASS   -8.69961    2.35099  288.49370  -3.700 0.000258 ***
degreeMASTERS                   -0.33621    2.10936  280.44980  -0.159 0.873477    
degreeMASTERS +                 -2.37697    5.96377  275.53135  -0.399 0.690520    
degreeSPECIALIST                19.25123   10.64910  405.76184   1.808 0.071381 .  
schoolmath                       0.99386    0.04374  275.01862  22.724  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation of Fixed Effects:
            (Intr) slfcnc cREGUC cRE+AC dMASTE dMAST+ dSPECI
selfconcept -0.274                                          
cREGULARCLA -0.039  0.030                                   
cREGULAR+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       
schoolmath  -0.951 -0.025 -0.019  0.002 -0.043 -0.030 -0.014
convergence code: 0
boundary (singular) fit: see ?isSingular

#checking effect size for model 2 (I don’t think I need to check it here but my last model before random slopes?)

rand(model.2)
ANOVA-like table for random-effects: Single term deletions

Model:
math ~ selfconcept + classtype + degree + (1 | classid) + (1 | 
    schoolid)
               npar logLik   AIC    LRT Df Pr(>Chisq)    
<none>           10 -24471 48961                         
(1 | classid)     9 -24592 49202 242.82  1  < 2.2e-16 ***
(1 | schoolid)    9 -24521 49060 101.04  1  < 2.2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

#checking effect size for model 3

rand(model.3)
boundary (singular) fit: see ?isSingular
ANOVA-like table for random-effects: Single term deletions

Model:
math ~ selfconcept + classtype + degree + schoolmath + (1 | classid) + 
    (1 | schoolid)
               npar logLik   AIC    LRT Df Pr(>Chisq)    
<none>           11 -24373 48768                         
(1 | classid)    10 -24465 48949 183.04  1     <2e-16 ***
(1 | schoolid)   10 -24373 48766   0.00  1          1    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

#Running random slope for self-concept (selfconcept) at the teacher/class level.

model.4 <- lmer(math~selfconcept + classtype + degree + schoolmath + (selfconcept|classid) + (1|schoolid), REML=FALSE, data=star.clean)
unable to evaluate scaled gradientModel failed to converge: degenerate  Hessian with 1 negative eigenvaluesModel failed to converge with 1 negative eigenvalue: -9.6e+00
summary(model.4)
Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's method ['lmerModLmerTest']
Formula: math ~ selfconcept + classtype + degree + schoolmath + (selfconcept |  
    classid) + (1 | schoolid)
   Data: star.clean

     AIC      BIC   logLik deviance df.resid 
 48770.8  48854.9 -24372.4  48744.8     4743 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-3.7969 -0.6429 -0.0614  0.5912  4.0142 

Random effects:
 Groups   Name        Variance  Std.Dev. Corr 
 classid  (Intercept) 3.485e+02 18.6695       
          selfconcept 6.847e-02  0.2617  -0.71
 schoolid (Intercept) 9.128e-02  0.3021       
 Residual             1.551e+03 39.3882       
Number of obs: 4756, groups:  classid, 301; schoolid, 73

Fixed effects:
                               Estimate Std. Error        df t value Pr(>|t|)    
(Intercept)                    -14.4199    22.0405  318.1812  -0.654 0.513427    
selfconcept                      0.4388     0.1187 2037.8827   3.697 0.000224 ***
classtypeREGULAR CLASS          -8.1850     2.3432  296.0238  -3.493 0.000551 ***
classtypeREGULAR + AIDE CLASS   -8.6691     2.3425  291.1453  -3.701 0.000257 ***
degreeMASTERS                   -0.3135     2.1019  282.3378  -0.149 0.881551    
degreeMASTERS +                 -2.2290     5.9444  277.3880  -0.375 0.707968    
degreeSPECIALIST                19.3272    10.6314  396.6436   1.818 0.069828 .  
schoolmath                       0.9940     0.0436  273.2880  22.796  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation of Fixed Effects:
            (Intr) slfcnc cREGUC cRE+AC dMASTE dMAST+ dSPECI
selfconcept -0.277                                          
cREGULARCLA -0.040  0.032                                   
cREGULAR+AC -0.060  0.028  0.480                            
degrMASTERS  0.019 -0.011 -0.072 -0.064                     
dgrMASTERS+  0.021 -0.006 -0.022 -0.001  0.114              
dSPECIALIST  0.003 -0.008  0.101  0.101  0.053  0.021       
schoolmath  -0.950 -0.027 -0.019  0.002 -0.043 -0.030 -0.014
convergence code: 0
unable to evaluate scaled gradient
Model failed to converge: degenerate  Hessian with 1 negative eigenvalues

#Running random slope for self-concept (selfconcept) at the school level.

model.5 <- lmer(math~selfconcept + classtype + degree + schoolmath + (1|classid) + (selfconcept|schoolid), REML=FALSE, data=star.clean)
boundary (singular) fit: see ?isSingular
summary(model.5)
Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's method ['lmerModLmerTest']
Formula: math ~ selfconcept + classtype + degree + schoolmath + (1 | classid) +  
    (selfconcept | schoolid)
   Data: star.clean

     AIC      BIC   logLik deviance df.resid 
 48763.3  48847.4 -24368.6  48737.3     4743 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-3.7454 -0.6503 -0.0607  0.5866  4.0344 

Random effects:
 Groups   Name        Variance  Std.Dev. Corr 
 classid  (Intercept)  169.4817 13.0185       
 schoolid (Intercept) 1733.5612 41.6361       
          selfconcept    0.5549  0.7449  -1.00
 Residual             1540.9570 39.2550       
Number of obs: 4756, groups:  classid, 301; schoolid, 73

Fixed effects:
                               Estimate Std. Error        df t value Pr(>|t|)    
(Intercept)                   -14.19106   22.49511 324.23626  -0.631 0.528582    
selfconcept                     0.41450    0.14949  64.96742   2.773 0.007245 ** 
classtypeREGULAR CLASS         -8.28684    2.33591 298.05015  -3.548 0.000451 ***
classtypeREGULAR + AIDE CLASS  -8.67911    2.33323 292.28934  -3.720 0.000239 ***
degreeMASTERS                  -0.59336    2.09262 283.66571  -0.284 0.776964    
degreeMASTERS +                -2.55123    5.92240 279.49950  -0.431 0.666963    
degreeSPECIALIST               19.55020   10.59636 414.03966   1.845 0.065753 .  
schoolmath                      0.99669    0.04336 277.31610  22.988  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation of Fixed Effects:
            (Intr) slfcnc cREGUC cRE+AC dMASTE dMAST+ dSPECI
selfconcept -0.352                                          
cREGULARCLA -0.040  0.027                                   
cREGULAR+AC -0.058  0.023  0.481                            
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       
schoolmath  -0.925 -0.023 -0.019  0.002 -0.043 -0.029 -0.014
convergence code: 0
boundary (singular) fit: see ?isSingular

#checking to see if random slopes was fruitful

anova(model.3,model.4)
Data: star.clean
Models:
model.3: math ~ selfconcept + classtype + degree + schoolmath + (1 | classid) + 
model.3:     (1 | schoolid)
model.4: math ~ selfconcept + classtype + degree + schoolmath + (selfconcept | 
model.4:     classid) + (1 | schoolid)
        npar   AIC   BIC logLik deviance Chisq Df Pr(>Chisq)
model.3   11 48768 48839 -24373    48746                    
model.4   13 48771 48855 -24372    48745 1.353  2     0.5084

#checking to see if rand slopes was good for second slope.

anova(model.3, model.5)
Data: star.clean
Models:
model.3: math ~ selfconcept + classtype + degree + schoolmath + (1 | classid) + 
model.3:     (1 | schoolid)
model.5: math ~ selfconcept + classtype + degree + schoolmath + (1 | classid) + 
model.5:     (selfconcept | schoolid)
        npar   AIC   BIC logLik deviance  Chisq Df Pr(>Chisq)  
model.3   11 48768 48839 -24373    48746                       
model.5   13 48763 48847 -24369    48737 8.8782  2    0.01181 *
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
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