Research questions

Latent change score (LCS) models is a statistical framework for teasing apart the complex processes underlying development using longitudinal data. It helps to study how intra-individual characteristics develop, interact, and give rise to inter-individual variability (Kievit et al., 2018). Here implemented multiple-indicator LCS models address several questions, namely: (1) Do individual differences in non-cognitive factors like motivation or self-concept precede changes in academic achievement or (2) it is the case that prior level of academic achievement brings about changes in motivation and self-concept in course of schooling within lower secondary education? That is, can the change in one domain be considered a function of the starting level in the other? (3) How does these effects differ in students attending basic school vs. eight-year academies featuring academic tracking? (4) Is there a reliable inter-individual change in motivation, self-concept, and academic achievement and which of the school types is associated with larger gains (controlling for SES of the students)? (5) Is the amount of change in both domains dependent on their initial state and how does it differ by type of school? (6) Do the students reliably differ in their change in non-cognitive domains and scholastic achievement that they manifest over time? (7) Is there an association between the rate of change in the studied domains? I.e., do the degrees of changes co-occur after taking into account the coupling pathways (e.g., those with greater gains in motivation and self-concept exhibit larger improvements in achievement)?

To test the hypotheses of differential gain in non-cognitive domains and academic achievement for the two school types, we used multiple indicators to measure the respective constructs.

Statistical analysis was carried out in R, version 3.4.3, using packages lavaan, lavaan.survey, semPlot, dplyr, psych, ICC, Amelia, BaylorEdPsych, haven, survey, semTools, knitr, kableExtra, naniar, and ggplot2.

Sample characteristics

Number of students who did not respond to more than 2/3 or SAL items in both waves

## [1] 11

N

## [1] 5245

Gender

## 
##    1    2 
## 1403 1417

Gender == 1 (Girls) represents 49.75% of the sample. However, there is large missingness in the gender variable.

Age in years in 6th grade

Mean

## [1] 11.81159

SD

## [1] 0.3905147

Percentage of missing data

There is very little missing data. Regardless of what imputation procedure is applied, it won’t have much effect.

## [1] "0.535%"

Ns for basic schools and eight-year academies

## 
##   VG   ZS 
## 1480 3765

Descriptive stats and data viz

Descriptive statistics

Practically all the items are left skewed. Children choose answer option “Strongly disagree” infrequently - usually some ~5-6%.

vars n mean sd skew kurtosis se
C6_B1A 1 5245 2.55 0.73 0.25 -0.37 0.01
r9_B1A 2 5245 2.56 0.77 0.21 -0.45 0.01
C6_B1B 3 5245 2.98 0.82 -0.26 -0.84 0.01
r9_B1B 4 5245 2.85 0.88 -0.17 -0.89 0.01
C6_B1C 5 5245 3.36 0.78 -0.97 0.09 0.01
r9_B1C 6 5245 3.07 0.87 -0.53 -0.64 0.01
C6_B1D 7 5245 2.96 0.82 -0.30 -0.67 0.01
r9_B1D 8 5245 2.53 0.83 0.11 -0.56 0.01
C6_B1E 9 5245 2.61 0.77 0.09 -0.47 0.01
r9_B1E 10 5245 2.47 0.85 0.22 -0.60 0.01
C6_B1F 11 5245 2.93 0.85 -0.36 -0.58 0.01
r9_B1F 12 5245 2.92 0.86 -0.30 -0.74 0.01
C6_B1G 13 5245 3.08 0.80 -0.41 -0.65 0.01
r9_B1G 14 5245 2.78 0.83 -0.09 -0.69 0.01
C6_B1H 15 5245 3.18 0.92 -0.82 -0.35 0.01
r9_B1H 16 5245 2.90 0.97 -0.42 -0.88 0.01
C6_B1I 17 5245 2.71 0.80 -0.04 -0.56 0.01
r9_B1I 18 5245 2.31 0.80 0.20 -0.40 0.01
C6_B1J 19 5245 2.92 0.80 -0.23 -0.63 0.01
r9_B1J 20 5245 2.82 0.82 -0.14 -0.68 0.01
C6_B1K 21 5245 3.23 0.77 -0.61 -0.44 0.01
r9_B1K 22 5245 2.91 0.80 -0.23 -0.61 0.01
C6_B1L 23 5245 3.51 0.73 -1.38 1.14 0.01
r9_B1L 24 5245 3.33 0.82 -1.02 0.20 0.01
C6_B1M 25 5245 3.22 0.74 -0.55 -0.47 0.01
r9_B1M 26 5245 3.17 0.76 -0.52 -0.45 0.01
C6_B1N 27 5245 3.16 0.74 -0.40 -0.65 0.01
r9_B1N 28 5245 3.00 0.77 -0.21 -0.76 0.01
C6_B1O 29 5245 3.31 0.75 -0.72 -0.32 0.01
r9_B1O 30 5245 2.86 0.81 -0.13 -0.73 0.01
C6_B2A 31 5245 2.80 0.92 -0.30 -0.77 0.01
r9x_B2A 32 5245 2.38 0.97 0.16 -0.94 0.01
C6_B2B 33 5245 3.06 0.70 -0.39 0.06 0.01
r9x_B2B 34 5245 2.91 0.68 -0.23 -0.03 0.01
C6_B2C 35 5245 2.82 0.91 -0.33 -0.74 0.01
r9x_B2C 36 5245 2.72 0.84 -0.22 -0.53 0.01
C6_B2D 37 5245 2.82 0.89 -0.33 -0.67 0.01
r9x_B2D 38 5245 3.03 0.80 -0.58 -0.04 0.01
C6_B2E 39 5245 2.85 1.02 -0.43 -0.98 0.01
r9x_B2E 40 5245 2.51 1.11 0.02 -1.35 0.02
C6_B2F 41 5245 3.18 0.66 -0.47 0.28 0.01
r9x_B2F 42 5245 3.02 0.65 -0.37 0.48 0.01
C6_B2G 43 5245 2.80 0.79 -0.30 -0.27 0.01
r9x_B2G 44 5245 2.77 0.79 -0.22 -0.39 0.01
C6_B2H 45 5245 2.93 1.00 -0.52 -0.84 0.01
r9x_B2H 46 5245 2.30 1.01 0.24 -1.03 0.01
C6_B2I 47 5245 3.00 0.84 -0.54 -0.30 0.01
r9x_B2I 48 5245 2.72 0.84 -0.24 -0.52 0.01
C6_B2J 49 5245 3.13 0.83 -0.67 -0.19 0.01
r9x_B2J 50 5245 2.68 0.95 -0.25 -0.85 0.01
C6_B2K 51 5245 2.68 1.01 -0.17 -1.07 0.01
r9x_B2K 52 5245 2.43 1.08 0.10 -1.25 0.01
C6_B2L 53 5245 2.79 1.07 -0.32 -1.19 0.01
r9x_B2L 54 5245 2.12 1.05 0.49 -0.99 0.01
C6_B2M 55 5245 3.51 0.73 -1.43 1.47 0.01
r9x_B2M 56 5245 3.42 0.77 -1.24 0.96 0.01
C6_B2N 57 5245 2.92 1.06 -0.52 -1.02 0.01
r9x_B2N 58 5245 2.69 1.14 -0.22 -1.38 0.02
C6_B2O 59 5245 3.00 0.89 -0.52 -0.58 0.01
r9x_B2O 60 5245 2.51 0.98 -0.02 -1.01 0.01
C6_B2P 61 5245 2.95 0.72 -0.32 -0.06 0.01
r9x_B2P 62 5245 2.94 0.66 -0.24 0.06 0.01
C6_B2Q 63 5245 3.19 0.85 -0.83 0.01 0.01
r9x_B2Q 64 5245 2.79 0.90 -0.30 -0.69 0.01
C6_B2R 65 5245 2.84 0.81 -0.33 -0.35 0.01
r9x_B2R 66 5245 2.87 0.78 -0.34 -0.23 0.01
C6_B2S 67 5245 2.75 0.86 -0.23 -0.60 0.01
r9x_B2S 68 5245 2.53 0.80 0.02 -0.47 0.01

Polychoric correlation heatmap for 6th grade

Polychoric correlation heatmap for 9th grade

Polychoric correlation heatmap for 6th and 9th grade

Results

SAL constructs and achievement by type of school and grade

Vertical dashed lines denote distribution means

Notes

1 Talking raw change, approx same change in achievement, 2 Variability in VG stays the same, in ZS, it gets larger, 3 both groups differ by about 1SD and also improve by about >1SD, 4 same rate of decline in both groups for most constructs, a bit more pronounced decline in EFFPER, INSMOT, INTMAT, SCMATH, and SCACAD (small effects).

ES of differences in motivation and self-concept

x
insmot6 0.0989240
insmot9 -0.0042419
effper6 0.1437006
effper9 0.0104881
selfef6 0.3464122
selfef9 0.3261807
cexp6 0.1904882
cexp9 0.1452674
intrea6 0.3633689
intrea9 0.3913509
intmat6 0.2003073
intmat9 0.0393809
comlrn6 0.1169952
comlrn9 0.0586160
scverb6 0.3207508
scverb9 0.1337630
scmath6 0.3198068
scmath9 0.2040643
scacad6 0.2967687
scacad9 0.1795113

Distributions for motivation and self-concept

Correlations between grades and achievement measures

1 Slightly larger correlation between achievement than grades, both high, generally, 2 Cor btw grades across 6 and 9 = .5 and .53., Cor btw achievement across 6 and 9 = ~.7, 3

grade.lang6 grade.lang9 grade.math6 grade.math9 lang_6 lang_9 math_6 math_9 lear_6 lear_9
grade.lang6 1.00 0.64 0.69 0.49 -0.62 -0.63 -0.55 -0.49 -0.49 -0.52
grade.lang9 0.64 1.00 0.50 0.68 -0.54 -0.62 -0.44 -0.44 -0.39 -0.46
grade.math6 0.69 0.50 1.00 0.53 -0.50 -0.51 -0.59 -0.55 -0.53 -0.56
grade.math9 0.49 0.68 0.53 1.00 -0.41 -0.50 -0.47 -0.53 -0.42 -0.51
lang_6 -0.62 -0.54 -0.50 -0.41 1.00 0.70 0.62 0.54 0.59 0.56
lang_9 -0.63 -0.62 -0.51 -0.50 0.70 1.00 0.57 0.57 0.55 0.61
math_6 -0.55 -0.44 -0.59 -0.47 0.62 0.57 1.00 0.72 0.72 0.70
math_9 -0.49 -0.44 -0.55 -0.53 0.54 0.57 0.72 1.00 0.70 0.76
lear_6 -0.49 -0.39 -0.53 -0.42 0.59 0.55 0.72 0.70 1.00 0.71
lear_9 -0.52 -0.46 -0.56 -0.51 0.56 0.61 0.70 0.76 0.71 1.00

Differences in correlations between ZS and VG

% smaller denotes how much smaller are the correlations in 8y academies students

1 Cor much smaller for VG, 2 Assessment in ZS much more consistent with actual achievement and has better prospective and retrospective validity (high cor btw grades6 and ach9, and vice versa)

MS 8YG % smaller r
grades6 grades9 0.68 0.42 0.62
grades6 achievement6 -0.64 -0.36 0.68
grades6 achievement9 -0.63 -0.35 0.69
grades9 achievement6 -0.62 -0.42 0.54
grades9 achievement9 -0.70 -0.49 0.51
achievement6 achievement9 0.78 0.71 0.17

ES of achievement difference

Grade 6

## [1] 1.374669

Grade 9

## [1] 0.8322678

Grade 6 -> 9 ZS

## [1] 1.052424

Grade 6 -> 9 VG

## [1] 1.29249

Means and SDs

label grade school grp.mean grp.sd
GPA 6th 8YG 1.167236 0.3322924
GPA 6th MS 1.846822 0.7179459
GPA 9th 8YG 1.947145 0.6702893
GPA 9th MS 2.247000 0.8477024

Distributions for achievement and GPA

BCSM diagram

BLCSM for INSMOT

Measurement invariance for INSMOT across grades

Invariance with respect to type of school in 6th grade

## 
## Measurement invariance models:
## 
## Model 1 : fit.configural
## Model 2 : fit.loadings
## Model 3 : fit.intercepts
## Model 4 : fit.means
## 
## Scaled Chi Square Difference Test (method = "satorra.bentler.2001")
## 
##                Df AIC BIC    Chisq Chisq diff Df diff Pr(>Chisq)    
## fit.configural 16           75.147                                  
## fit.loadings   20           89.084       25.5       4  3.995e-05 ***
## fit.intercepts 24          155.677      134.5       4  < 2.2e-16 ***
## fit.means      26         6150.261     3173.2       2  < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Fit measures:
## 
##                cfi.scaled rmsea.scaled cfi.scaled.delta rmsea.scaled.delta
## fit.configural      0.978        0.046               NA                 NA
## fit.loadings        0.973        0.046            0.005              0.000
## fit.intercepts      0.947        0.058            0.025              0.012
## fit.means           0.000        0.345            0.947              0.287

Invariance with respect to type of school in 9th grade

## 
## Measurement invariance models:
## 
## Model 1 : fit.configural
## Model 2 : fit.loadings
## Model 3 : fit.intercepts
## Model 4 : fit.means
## 
## Scaled Chi Square Difference Test (method = "satorra.bentler.2001")
## 
##                Df AIC BIC   Chisq Chisq diff Df diff Pr(>Chisq)    
## fit.configural 16          138.27                                  
## fit.loadings   20          168.94      65.83       4  1.721e-13 ***
## fit.intercepts 24          204.08      73.40       4  4.342e-15 ***
## fit.means      26         4869.10    2222.54       2  < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Fit measures:
## 
##                cfi.scaled rmsea.scaled cfi.scaled.delta rmsea.scaled.delta
## fit.configural      0.966        0.067               NA                 NA
## fit.loadings        0.955        0.069            0.011              0.002
## fit.intercepts      0.943        0.070            0.012              0.002
## fit.means           0.000        0.313            0.943              0.242

The model applies the sampling weights (vaha69) and accounts for the two-level hierarchical structure of the data (children nested within classes nested within schools).

Model test and approximate fit indices

##          chisq.scaled             df.scaled         pvalue.scaled 
##               230.586                32.000                 0.000 
##            cfi.scaled            tli.scaled          rmsea.scaled 
##                 0.980                 0.974                 0.034 
## rmsea.ci.lower.scaled rmsea.ci.upper.scaled                  srmr 
##                 0.032                 0.037                 0.033 
##                  pnfi                   bic 
##                 0.629            138825.673

Main model parameters with BFs

lhs op rhs z pvalue est std.all BF10 Posterior
32 dINSMOT ~ INSMOT6 -21.64 0.00 -0.58 -0.47 5.451170e+91 1.00
31 dINSMOT ~ ACH6 2.56 0.01 0.06 0.06 5.500000e+00 0.85
30 dACH ~ ACH6 5.94 0.00 0.13 0.26 1.976731e+09 1.00
29 dACH ~ INSMOT6 1.95 0.05 0.03 0.06 2.000000e-01 0.17
34 dINSMOT ~~ dACH 7.42 0.00 0.04 0.25 4.898392e+19 1.00
33 INSMOT6 ~~ ACH6 4.87 0.00 0.03 0.10 1.364083e+06 1.00
15 dINSMOT ~1 17.81 0.00 1.66 2.58 NA NA
16 dINSMOT ~~ dINSMOT 21.68 0.00 0.33 0.78 NA NA
23 dACH ~1 6.04 0.00 0.38 1.20 NA NA
24 dACH ~~ dACH 11.46 0.00 0.09 0.91 NA NA
17 INSMOT6 ~1 207.94 0.00 3.34 6.37 NA NA
25 ACH6 ~1 -11.11 0.00 -0.33 -0.50 NA NA 
## $`Group 1`
## INSMOT6 INSMOT9    ACH6    ACH9 dINSMOT    dACH     SES 
##   3.325   3.047  -0.460  -0.022  -0.278   0.438   0.000 
## 
## $`Group 2`
## INSMOT6 INSMOT9    ACH6    ACH9 dINSMOT    dACH     SES 
##   3.460   3.115   0.482   1.003  -0.345   0.521   0.000

Model parameters per subgroup

Group 1 = ZS, Group 2 = VG

lhs op rhs group est se z std.all group.1 est.1 se.1 z.1 std.all.1
32 dINSMOT ~ INSMOT6 1 -0.588 0.030 -19.427 -0.488 2 -0.561 0.048 -11.755 -0.404
31 dINSMOT ~ ACH6 1 0.105 0.027 3.811 0.094 2 -0.152 0.054 -2.797 -0.094
30 dACH ~ ACH6 1 0.114 0.030 3.827 0.210 2 0.403 0.060 6.682 0.496
29 dACH ~ INSMOT6 1 0.034 0.020 1.702 0.058 2 0.007 0.026 0.249 0.009
34 dINSMOT ~~ dACH 1 0.045 0.007 6.874 0.262 2 0.023 0.010 2.331 0.136
33 INSMOT6 ~~ ACH6 1 0.034 0.007 4.832 0.117 2 -0.011 0.007 -1.604 -0.061
15 dINSMOT ~1 1 1.725 0.107 16.048 2.674 2 1.670 0.166 10.037 2.580
16 dINSMOT ~~ dINSMOT 1 0.320 0.017 19.221 0.768 2 0.349 0.028 12.493 0.833
23 dACH ~1 1 0.377 0.072 5.256 1.191 2 0.304 0.105 2.893 0.943
24 dACH ~~ dACH 1 0.093 0.009 10.086 0.931 2 0.079 0.014 5.823 0.756
17 INSMOT6 ~1 1 3.325 0.018 182.971 6.206 2 3.460 0.023 148.752 7.414
25 ACH6 ~1 1 -0.460 0.025 -18.468 -0.790 2 0.482 0.039 12.236 1.212

Likelihood ratio tests

Tests whether constraining the given parameter across both types of school results in a significantly worse fit (i.e., whether the parameter differs between the groups)

## $`dINSMOT~INSMOT6`
##                 Chisq diff Df diff Pr(>Chisq)
## fit.constrained    0.43876       1     0.5077
## 
## $`dINSMOT~ACH6`
##                 Chisq diff Df diff Pr(>Chisq)    
## fit.constrained     14.813       1  0.0001187 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## $`dACH~ACH6`
##                 Chisq diff Df diff Pr(>Chisq)    
## fit.constrained     13.751       1  0.0002087 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## $`dACH~INSMOT6`
##                 Chisq diff Df diff Pr(>Chisq)
## fit.constrained    0.74257       1     0.3888
## 
## $`dINSMOT~~dACH`
##                 Chisq diff Df diff Pr(>Chisq)  
## fit.constrained     2.8224       1    0.09295 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## $`INSMOT6 ~~ ACH6`
##                 Chisq diff Df diff Pr(>Chisq)    
## fit.constrained     18.208       1  1.981e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## $`dINSMOT ~ 1`
##                 Chisq diff Df diff Pr(>Chisq)
## fit.constrained    0.32922       1     0.5661
## 
## $`dACH ~ 1`
##                 Chisq diff Df diff Pr(>Chisq)
## fit.constrained    0.48307       1      0.487

BLCSM for EFFPER

Measurement invariance for EFFPER across grades

Invariance with respect to type of school in 6th grade

## 
## Measurement invariance models:
## 
## Model 1 : fit.configural
## Model 2 : fit.loadings
## Model 3 : fit.intercepts
## Model 4 : fit.means
## 
## Scaled Chi Square Difference Test (method = "satorra.bentler.2001")
## 
##                Df AIC BIC   Chisq Chisq diff Df diff Pr(>Chisq)    
## fit.configural 26          159.83                                  
## fit.loadings   31          186.19      41.27       5  8.277e-08 ***
## fit.intercepts 40          303.51     200.16       9  < 2.2e-16 ***
## fit.means      42         6160.92    2191.62       2  < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Fit measures:
## 
##                cfi.scaled rmsea.scaled cfi.scaled.delta rmsea.scaled.delta
## fit.configural      0.986        0.053               NA                 NA
## fit.loadings        0.983        0.053            0.003              0.000
## fit.intercepts      0.970        0.062            0.013              0.009
## fit.means           0.417        0.265            0.553              0.204

Invariance with respect to type of school in 9th grade

## 
## Measurement invariance models:
## 
## Model 1 : fit.configural
## Model 2 : fit.loadings
## Model 3 : fit.intercepts
## Model 4 : fit.means
## 
## Scaled Chi Square Difference Test (method = "satorra.bentler.2001")
## 
##                Df AIC BIC   Chisq Chisq diff Df diff Pr(>Chisq)    
## fit.configural 26          535.93                                  
## fit.loadings   31          626.37     137.18       5  < 2.2e-16 ***
## fit.intercepts 40          799.95     296.51       9  < 2.2e-16 ***
## fit.means      42         5202.68    1245.98       2  < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Fit measures:
## 
##                cfi.scaled rmsea.scaled cfi.scaled.delta rmsea.scaled.delta
## fit.configural      0.946        0.101               NA                 NA
## fit.loadings        0.936        0.101            0.010              0.000
## fit.intercepts      0.914        0.103            0.022              0.002
## fit.means           0.520        0.238            0.395              0.135

Model test and approximate fit indices

##          chisq.scaled             df.scaled         pvalue.scaled 
##               385.104                44.000                 0.000 
##            cfi.scaled            tli.scaled          rmsea.scaled 
##                 0.967                 0.962                 0.038 
## rmsea.ci.lower.scaled rmsea.ci.upper.scaled                  srmr 
##                 0.036                 0.041                 0.051 
##                  pnfi                   bic 
##                 0.684            158722.538

Main model parameters with BFs

lhs op rhs z pvalue est std.all BF10 Posterior
34 dEFFPER ~ EFFPER6 -25.30 0.00 -0.62 -0.59 1.987876e+120 1.00
33 dEFFPER ~ ACH6 1.54 0.12 0.03 0.03 1.000000e-01 0.09
32 dACH ~ ACH6 6.18 0.00 0.13 0.26 5.667135e+09 1.00
31 dACH ~ EFFPER6 0.79 0.43 0.01 0.03 2.000000e-02 0.02
36 dEFFPER ~~ dACH 7.91 0.00 0.04 0.27 2.252484e+20 1.00
35 EFFPER6 ~~ ACH6 5.20 0.00 0.04 0.11 5.879286e+06 1.00
17 dEFFPER ~1 18.97 0.00 1.42 2.41 NA NA
18 dEFFPER ~~ dEFFPER 22.01 0.00 0.23 0.66 NA NA
25 dACH ~1 7.81 0.00 0.45 1.43 NA NA
26 dACH ~~ dACH 11.55 0.00 0.09 0.91 NA NA
19 EFFPER6 ~1 171.57 0.00 2.97 5.28 NA NA
27 ACH6 ~1 -11.11 0.00 -0.33 -0.50 NA NA

Model parameters per subgroup

Group 1 = ZS, Group 2 = VG

lhs op rhs group est se z std.all group.1 est.1 se.1 z.1 std.all.1
34 dEFFPER ~ EFFPER6 1 -0.637 0.027 -23.761 -0.612 2 -0.518 0.037 -13.842 -0.491
33 dEFFPER ~ ACH6 1 0.071 0.024 2.954 0.071 2 -0.125 0.055 -2.262 -0.080
32 dACH ~ ACH6 1 0.119 0.029 4.067 0.218 2 0.401 0.058 6.978 0.496
31 dACH ~ EFFPER6 1 0.010 0.020 0.483 0.017 2 0.006 0.030 0.207 0.011
36 dEFFPER ~~ dACH 1 0.042 0.006 7.525 0.294 2 0.007 0.008 0.835 0.047
35 EFFPER6 ~~ ACH6 1 0.042 0.008 5.278 0.137 2 -0.013 0.008 -1.628 -0.057
17 dEFFPER ~1 1 1.520 0.084 18.173 2.592 2 1.068 0.120 8.867 1.719
18 dEFFPER ~~ dEFFPER 1 0.219 0.011 19.481 0.636 2 0.289 0.018 15.881 0.750
25 dACH ~1 1 0.463 0.066 6.977 1.463 2 0.309 0.099 3.118 0.958
26 dACH ~~ dACH 1 0.093 0.009 10.110 0.932 2 0.079 0.013 5.949 0.756
19 EFFPER6 ~1 1 2.978 0.020 151.619 5.284 2 2.945 0.022 132.302 5.000
27 ACH6 ~1 1 -0.460 0.025 -18.468 -0.790 2 0.482 0.039 12.236 1.209

Likelihood ratio tests

Tests whether constraining the given parameter across both types of school results in a significantly worse fit (i.e., whether the parameter differs between the groups)

## $`dEFFPER~EFFPER6`
##                 Chisq diff Df diff Pr(>Chisq)  
## fit.constrained     5.6071       1    0.01789 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## $`dEFFPER~ACH6`
##                 Chisq diff Df diff Pr(>Chisq)   
## fit.constrained     8.2278       1   0.004125 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## $`dACH~ACH6`
##                 Chisq diff Df diff Pr(>Chisq)    
## fit.constrained     13.265       1  0.0002705 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## $`dACH~EFFPER6`
##                 Chisq diff Df diff Pr(>Chisq)
## fit.constrained    0.26848       1     0.6044
## 
## $`dEFFPER~~dACH`
##                 Chisq diff Df diff Pr(>Chisq)   
## fit.constrained     8.8049       1   0.003004 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## $`EFFPER6 ~~ ACH6`
##                 Chisq diff Df diff Pr(>Chisq)    
## fit.constrained     21.517       1  3.507e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## $`dEFFPER~1`
##                 Chisq diff Df diff Pr(>Chisq)   
## fit.constrained     7.8672       1   0.005034 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## $`dACH~1`
##                 Chisq diff Df diff Pr(>Chisq)
## fit.constrained     1.4392       1     0.2303

BLCSM for SELFEF

Measurement invariance for SELFEF across grades

Invariance with respect to type of school in 6th grade

## 
## Measurement invariance models:
## 
## Model 1 : fit.configural
## Model 2 : fit.loadings
## Model 3 : fit.intercepts
## Model 4 : fit.means
## 
## Scaled Chi Square Difference Test (method = "satorra.bentler.2001")
## 
##                Df AIC BIC   Chisq Chisq diff Df diff Pr(>Chisq)    
## fit.configural 26          187.71                                  
## fit.loadings   31          215.51      34.37       5  2.012e-06 ***
## fit.intercepts 40          295.26     126.49       9  < 2.2e-16 ***
## fit.means      42         6466.77    1918.64       2  < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Fit measures:
## 
##                cfi.scaled rmsea.scaled cfi.scaled.delta rmsea.scaled.delta
## fit.configural      0.983        0.062               NA                 NA
## fit.loadings        0.981        0.060            0.002              0.003
## fit.intercepts      0.974        0.062            0.007              0.002
## fit.means           0.472        0.273            0.502              0.210

Invariance with respect to type of school in 9th grade

## 
## Measurement invariance models:
## 
## Model 1 : fit.configural
## Model 2 : fit.loadings
## Model 3 : fit.intercepts
## Model 4 : fit.means
## 
## Scaled Chi Square Difference Test (method = "satorra.bentler.2001")
## 
##                Df AIC BIC   Chisq Chisq diff Df diff Pr(>Chisq)    
## fit.configural 26          128.04                                  
## fit.loadings   31          154.63      25.57       5  0.0001081 ***
## fit.intercepts 40          212.62      94.10       9  2.441e-16 ***
## fit.means      42         4998.29    1139.62       2  < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Fit measures:
## 
##                cfi.scaled rmsea.scaled cfi.scaled.delta rmsea.scaled.delta
## fit.configural      0.989        0.057               NA                 NA
## fit.loadings        0.989        0.053            0.000              0.004
## fit.intercepts      0.985        0.054            0.004              0.002
## fit.means           0.683        0.240            0.302              0.186

Model test and approximate fit indices

##          chisq.scaled             df.scaled         pvalue.scaled 
##               297.768                42.000                 0.000 
##            cfi.scaled            tli.scaled          rmsea.scaled 
##                 0.976                 0.972                 0.034 
## rmsea.ci.lower.scaled rmsea.ci.upper.scaled                  srmr 
##                 0.032                 0.036                 0.026 
##                  pnfi                   bic 
##                 0.689            153173.074

Main model parameters with BFs

lhs op rhs z pvalue est std.all BF10 Posterior
34 dSELFEF ~ SELFEF6 -25.28 0.00 -0.57 -0.59 2.078982e+110 1.00
33 dSELFEF ~ ACH6 14.29 0.00 0.24 0.31 1.871396e+60 1.00
32 dACH ~ ACH6 5.70 0.00 0.13 0.26 5.899708e+08 1.00
31 dACH ~ SELFEF6 1.37 0.17 0.03 0.04 5.000000e-02 0.04
36 dSELFEF ~~ dACH 8.43 0.00 0.04 0.34 5.425954e+31 1.00
35 SELFEF6 ~~ ACH6 14.87 0.00 0.09 0.32 6.206550e+73 1.00
17 dSELFEF ~1 25.26 0.00 1.52 3.04 NA NA
18 dSELFEF ~~ dSELFEF 20.13 0.00 0.17 0.68 NA NA
25 dACH ~1 7.66 0.00 0.42 1.34 NA NA
26 dACH ~~ dACH 11.51 0.00 0.09 0.91 NA NA
19 SELFEF6 ~1 165.80 0.00 2.52 4.90 NA NA
27 ACH6 ~1 -11.11 0.00 -0.33 -0.50 NA NA

Model parameters per subgroup

Group 1 = ZS, Group 2 = VG

lhs op rhs group est se z std.all group.1 est.1 se.1 z.1 std.all.1
34 dSELFEF ~ SELFEF6 1 -0.577 0.025 -23.042 -0.598 2 -0.642 0.042 -15.205 -0.597
33 dSELFEF ~ ACH6 1 0.298 0.020 15.293 0.359 2 0.223 0.048 4.613 0.164
32 dACH ~ ACH6 1 0.116 0.031 3.698 0.212 2 0.426 0.062 6.853 0.518
31 dACH ~ SELFEF6 1 0.032 0.022 1.433 0.050 2 -0.056 0.039 -1.434 -0.086
36 dSELFEF ~~ dACH 1 0.042 0.006 7.373 0.341 2 0.029 0.009 3.173 0.229
35 SELFEF6 ~~ ACH6 1 0.091 0.007 12.404 0.330 2 0.044 0.008 5.793 0.224
17 dSELFEF ~1 1 1.567 0.067 23.501 3.215 2 1.667 0.116 14.427 3.064
18 dSELFEF ~~ dSELFEF 1 0.157 0.009 17.427 0.660 2 0.192 0.017 11.168 0.649
25 dACH ~1 1 0.412 0.066 6.238 1.284 2 0.469 0.108 4.347 1.422
26 dACH ~~ dACH 1 0.095 0.009 10.158 0.926 2 0.081 0.014 5.934 0.746
19 SELFEF6 ~1 1 2.479 0.016 150.574 4.903 2 2.732 0.024 115.755 5.404
27 ACH6 ~1 1 -0.460 0.025 -18.468 -0.785 2 0.482 0.039 12.236 1.202

Likelihood ratio tests

Tests whether constraining the given parameter across both types of school results in a significantly worse fit (i.e., whether the parameter differs between the groups)

## $`dSELFEF~SELFEF6`
##                 Chisq diff Df diff Pr(>Chisq)
## fit.constrained     1.4397       1     0.2302
## 
## $`dSELFEF~ACH6`
##                 Chisq diff Df diff Pr(>Chisq)
## fit.constrained     1.5395       1     0.2147
## 
## $`dACH~ACH6`
##                 Chisq diff Df diff Pr(>Chisq)    
## fit.constrained     16.417       1  5.082e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## $`dACH~SELFEF6`
##                 Chisq diff Df diff Pr(>Chisq)  
## fit.constrained     2.8501       1    0.09137 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## $`dSELFEF~~dACH`
##                 Chisq diff Df diff Pr(>Chisq)
## fit.constrained     1.3109       1     0.2522
## 
## $`SELFEF6 ~~ ACH6`
##                 Chisq diff Df diff Pr(>Chisq)    
## fit.constrained     15.444       1  8.496e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## $`dSELFEF~1`
##                 Chisq diff Df diff Pr(>Chisq)
## fit.constrained     0.6742       1     0.4116
## 
## $`dACH~1`
##                 Chisq diff Df diff Pr(>Chisq)
## fit.constrained    0.43259       1     0.5107

BLCSM for CEXP

Measurement invariance for CEXP across grades

Invariance with respect to type of school in 6th grade

## 
## Measurement invariance models:
## 
## Model 1 : fit.configural
## Model 2 : fit.loadings
## Model 3 : fit.intercepts
## Model 4 : fit.means
## 
## Scaled Chi Square Difference Test (method = "satorra.bentler.2001")
## 
##                Df AIC BIC    Chisq Chisq diff Df diff Pr(>Chisq)    
## fit.configural 26           83.762                                  
## fit.loadings   31          113.766      44.55       5  1.793e-08 ***
## fit.intercepts 40          172.705      95.76       9  < 2.2e-16 ***
## fit.means      42         6056.470    2145.05       2  < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Fit measures:
## 
##                cfi.scaled rmsea.scaled cfi.scaled.delta rmsea.scaled.delta
## fit.configural      0.992        0.036               NA                 NA
## fit.loadings        0.989        0.039            0.003              0.003
## fit.intercepts      0.982        0.044            0.007              0.005
## fit.means           0.336        0.260            0.646              0.216

Invariance with respect to type of school in 9th grade

## 
## Measurement invariance models:
## 
## Model 1 : fit.configural
## Model 2 : fit.loadings
## Model 3 : fit.intercepts
## Model 4 : fit.means
## 
## Scaled Chi Square Difference Test (method = "satorra.bentler.2001")
## 
##                Df AIC BIC   Chisq Chisq diff Df diff Pr(>Chisq)    
## fit.configural 26          146.88                                  
## fit.loadings   31          172.54      30.09       5  1.414e-05 ***
## fit.intercepts 40          206.06      53.26       9  2.613e-08 ***
## fit.means      42         4692.14    1293.39       2  < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Fit measures:
## 
##                cfi.scaled rmsea.scaled cfi.scaled.delta rmsea.scaled.delta
## fit.configural      0.985        0.055               NA                 NA
## fit.loadings        0.983        0.053            0.002              0.002
## fit.intercepts      0.980        0.051            0.003              0.002
## fit.means           0.563        0.230            0.416              0.179

Model test and approximate fit indices

##          chisq.scaled             df.scaled         pvalue.scaled 
##               208.821                43.000                 0.000 
##            cfi.scaled            tli.scaled          rmsea.scaled 
##                 0.983                 0.980                 0.027 
## rmsea.ci.lower.scaled rmsea.ci.upper.scaled                  srmr 
##                 0.025                 0.029                 0.025 
##                  pnfi                   bic 
##                 0.693            161384.565

Main model parameters with BFs

lhs op rhs z pvalue est std.all BF10 Posterior
34 dCEXP ~ CEXP6 -17.55 0.00 -0.51 -0.48 1.301478e+75 1.00
33 dCEXP ~ ACH6 7.83 0.00 0.18 0.19 3.792941e+20 1.00
32 dACH ~ ACH6 5.82 0.00 0.13 0.26 3.026852e+09 1.00
31 dACH ~ CEXP6 0.61 0.54 0.01 0.02 2.000000e-02 0.02
36 dCEXP ~~ dACH 7.61 0.00 0.05 0.29 9.575896e+21 1.00
35 CEXP6 ~~ ACH6 7.97 0.00 0.06 0.17 3.480677e+19 1.00
17 dCEXP ~1 16.06 0.00 1.45 2.37 NA NA
18 dCEXP ~~ dCEXP 26.79 0.00 0.29 0.77 NA NA
25 dACH ~1 8.55 0.00 0.46 1.47 NA NA
26 dACH ~~ dACH 11.41 0.00 0.09 0.91 NA NA
19 CEXP6 ~1 170.59 0.00 2.95 5.15 NA NA
27 ACH6 ~1 -11.11 0.00 -0.33 -0.50 NA NA

Model parameters per subgroup

Group 1 = ZS, Group 2 = VG

lhs op rhs group est se z std.all group.1 est.1 se.1 z.1 std.all.1
34 dCEXP ~ CEXP6 1 -0.531 0.032 -16.582 -0.507 2 -0.438 0.048 -9.150 -0.352
33 dCEXP ~ ACH6 1 0.244 0.026 9.427 0.233 2 0.096 0.054 1.786 0.065
32 dACH ~ ACH6 1 0.117 0.031 3.792 0.216 2 0.406 0.061 6.696 0.500
31 dACH ~ CEXP6 1 0.009 0.018 0.473 0.016 2 -0.023 0.040 -0.566 -0.033
36 dCEXP ~~ dACH 1 0.046 0.007 6.620 0.286 2 0.034 0.009 3.559 0.216
35 CEXP6 ~~ ACH6 1 0.061 0.008 7.222 0.192 2 0.011 0.008 1.399 0.059
17 dCEXP ~1 1 1.540 0.099 15.598 2.525 2 1.174 0.152 7.711 1.961
18 dCEXP ~~ dCEXP 1 0.274 0.011 23.915 0.735 2 0.307 0.021 14.609 0.857
25 dACH ~1 1 0.467 0.063 7.432 1.474 2 0.396 0.128 3.094 1.216
26 dACH ~~ dACH 1 0.093 0.009 10.035 0.933 2 0.080 0.014 5.745 0.753
19 CEXP6 ~1 1 2.921 0.019 150.862 5.019 2 3.119 0.021 145.353 6.485
27 ACH6 ~1 1 -0.460 0.025 -18.468 -0.789 2 0.482 0.039 12.236 1.204

Likelihood ratio tests

Tests whether constraining the given parameter across both types of school results in a significantly worse fit (i.e., whether the parameter differs between the groups)

## $`dCEXP~CEXP6`
##                 Chisq diff Df diff Pr(>Chisq)
## fit.constrained     2.2101       1     0.1371
## 
## $`dCEXP~ACH6`
##                 Chisq diff Df diff Pr(>Chisq)  
## fit.constrained     3.9802       1    0.04604 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## $`dACH~ACH6`
##                 Chisq diff Df diff Pr(>Chisq)    
## fit.constrained      13.81       1  0.0002023 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## $`dACH~CEXP6`
##                 Chisq diff Df diff Pr(>Chisq)
## fit.constrained    0.67572       1     0.4111
## 
## $`dCEXP~~dACH`
##                 Chisq diff Df diff Pr(>Chisq)
## fit.constrained    0.98291       1     0.3215
## 
## $`CEXP6 ~~ ACH6`
##                 Chisq diff Df diff Pr(>Chisq)    
## fit.constrained     16.532       1  4.784e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## $`dCEXP~1`
##                 Chisq diff Df diff Pr(>Chisq)  
## fit.constrained     3.3549       1      0.067 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## $`dACH~1`
##                 Chisq diff Df diff Pr(>Chisq)
## fit.constrained    0.50967       1     0.4753

BLCSM for INTREA

Measurement invariance for INTREA across grades

Invariance with respect to type of school in 6th grade

## 
## Measurement invariance models:
## 
## Model 1 : fit.configural
## Model 2 : fit.loadings
## Model 3 : fit.intercepts
## Model 4 : fit.means
## 
## Scaled Chi Square Difference Test (method = "satorra.bentler.2001")
## 
##                Df AIC BIC   Chisq Chisq diff Df diff Pr(>Chisq)    
## fit.configural 16          164.74                                  
## fit.loadings   20          188.41      32.71       4  1.369e-06 ***
## fit.intercepts 27          205.40      34.41       7  1.442e-05 ***
## fit.means      29         6566.88    1642.39       2  < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Fit measures:
## 
##                cfi.scaled rmsea.scaled cfi.scaled.delta rmsea.scaled.delta
## fit.configural      0.992        0.077               NA                 NA
## fit.loadings        0.991        0.072            0.001              0.005
## fit.intercepts      0.990        0.067            0.001              0.006
## fit.means           0.741        0.321            0.249              0.255

Invariance with respect to type of school in 9th grade

## 
## Measurement invariance models:
## 
## Model 1 : fit.configural
## Model 2 : fit.loadings
## Model 3 : fit.intercepts
## Model 4 : fit.means
## 
## Scaled Chi Square Difference Test (method = "satorra.bentler.2001")
## 
##                Df AIC BIC   Chisq Chisq diff Df diff Pr(>Chisq)    
## fit.configural 16          378.54                                  
## fit.loadings   20          392.62      21.87       4  0.0002131 ***
## fit.intercepts 27          402.68      22.65       7  0.0019602 ** 
## fit.means      29         5598.79     860.77       2  < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Fit measures:
## 
##                cfi.scaled rmsea.scaled cfi.scaled.delta rmsea.scaled.delta
## fit.configural      0.990        0.119               NA                 NA
## fit.loadings        0.990        0.108            0.000              0.011
## fit.intercepts      0.989        0.098            0.001              0.010
## fit.means           0.904        0.278            0.085              0.180

Model test and approximate fit indices

##          chisq.scaled             df.scaled         pvalue.scaled 
##               263.497                33.000                 0.000 
##            cfi.scaled            tli.scaled          rmsea.scaled 
##                 0.983                 0.979                 0.036 
## rmsea.ci.lower.scaled rmsea.ci.upper.scaled                  srmr 
##                 0.034                 0.039                 0.045 
##                  pnfi                   bic 
##                 0.632            143769.877

Main model parameters with BFs

lhs op rhs z pvalue est std.all BF10 Posterior
32 dINTREA ~ INTREA6 -18.30 0.00 -0.38 -0.38 2.207422e+84 1.00
31 dINTREA ~ ACH6 5.94 0.00 0.15 0.11 4.919580e+07 1.00
30 dACH ~ ACH6 5.98 0.00 0.13 0.26 6.578010e+09 1.00
29 dACH ~ INTREA6 -0.51 0.61 -0.01 -0.02 2.000000e-02 0.02
34 dINTREA ~~ dACH 3.81 0.00 0.03 0.12 4.835400e+02 1.00
33 INTREA6 ~~ ACH6 5.17 0.00 0.05 0.09 2.397464e+05 1.00
15 dINTREA ~1 11.68 0.00 0.74 0.84 NA NA
16 dINTREA ~~ dINTREA 30.65 0.00 0.65 0.86 NA NA
23 dACH ~1 13.74 0.00 0.51 1.61 NA NA
24 dACH ~~ dACH 11.50 0.00 0.09 0.91 NA NA
17 INTREA6 ~1 124.43 0.00 2.80 3.21 NA NA
25 ACH6 ~1 -11.11 0.00 -0.33 -0.50 NA NA

Model parameters per subgroup

Group 1 = ZS, Group 2 = VG

lhs op rhs group est se z std.all group.1 est.1 se.1 z.1 std.all.1
32 dINTREA ~ INTREA6 1 -0.383 0.024 -16.302 -0.381 2 -0.354 0.030 -11.800 -0.350
31 dINTREA ~ ACH6 1 0.139 0.031 4.450 0.093 2 0.051 0.076 0.672 0.024
30 dACH ~ ACH6 1 0.118 0.030 3.905 0.216 2 0.408 0.061 6.676 0.507
29 dACH ~ INTREA6 1 0.000 0.012 0.003 0.000 2 -0.028 0.023 -1.224 -0.073
34 dINTREA ~~ dACH 1 0.034 0.008 4.014 0.137 2 -0.001 0.011 -0.054 -0.003
33 INTREA6 ~~ ACH6 1 0.024 0.010 2.327 0.051 2 0.058 0.014 4.298 0.178
15 dINTREA ~1 1 0.728 0.072 10.162 0.837 2 0.793 0.097 8.203 0.917
16 dINTREA ~~ dINTREA 1 0.646 0.024 26.630 0.855 2 0.659 0.030 21.769 0.883
23 dACH ~1 1 0.492 0.042 11.782 1.553 2 0.410 0.074 5.560 1.271
24 dACH ~~ dACH 1 0.094 0.009 10.068 0.934 2 0.078 0.013 5.845 0.753
17 INTREA6 ~1 1 2.750 0.024 114.103 3.180 2 3.094 0.032 95.402 3.619
25 ACH6 ~1 1 -0.460 0.025 -18.468 -0.790 2 0.482 0.039 12.236 1.201

Likelihood ratio tests

Tests whether constraining the given parameter across both types of school results in a significantly worse fit (i.e., whether the parameter differs between the groups)

## $`dINTREA~INTREA6`
##                 Chisq diff Df diff Pr(>Chisq)
## fit.constrained    0.65408       1     0.4187
## 
## $`dINTREA~ACH6`
##                 Chisq diff Df diff Pr(>Chisq)
## fit.constrained     1.0124       1     0.3143
## 
## $`dACH~ACH6`
##                 Chisq diff Df diff Pr(>Chisq)    
## fit.constrained     12.798       1   0.000347 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## $`dACH~INTREA6`
##                 Chisq diff Df diff Pr(>Chisq)
## fit.constrained     1.1003       1     0.2942
## 
## $`dINTREA~~dACH`
##                 Chisq diff Df diff Pr(>Chisq)  
## fit.constrained     4.5495       1    0.03293 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## $`INTREA6 ~~ ACH6`
##                 Chisq diff Df diff Pr(>Chisq)  
## fit.constrained     3.4984       1    0.06143 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## $`dINTREA~1`
##                 Chisq diff Df diff Pr(>Chisq)
## fit.constrained     0.4421       1     0.5061
## 
## $`dACH~1`
##                 Chisq diff Df diff Pr(>Chisq)
## fit.constrained    0.93567       1     0.3334

BLCSM for INTMAT

Measurement invariance for INTMAT across grades

Invariance with respect to type of school in 6th grade

## 
## Measurement invariance models:
## 
## Model 1 : fit.configural
## Model 2 : fit.loadings
## Model 3 : fit.intercepts
## Model 4 : fit.means
## 
## Scaled Chi Square Difference Test (method = "satorra.bentler.2001")
## 
##                Df AIC BIC   Chisq Chisq diff Df diff Pr(>Chisq)    
## fit.configural 16          208.59                                  
## fit.loadings   20          240.88      54.18       4  4.834e-11 ***
## fit.intercepts 27          299.20     106.54       7  < 2.2e-16 ***
## fit.means      29         6159.62    2260.78       2  < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Fit measures:
## 
##                cfi.scaled rmsea.scaled cfi.scaled.delta rmsea.scaled.delta
## fit.configural      0.975        0.080               NA                 NA
## fit.loadings        0.970        0.078            0.005              0.002
## fit.intercepts      0.960        0.077            0.010              0.001
## fit.means           0.279        0.318            0.681              0.240

Invariance with respect to type of school in 9th grade

## 
## Measurement invariance models:
## 
## Model 1 : fit.configural
## Model 2 : fit.loadings
## Model 3 : fit.intercepts
## Model 4 : fit.means
## 
## Scaled Chi Square Difference Test (method = "satorra.bentler.2001")
## 
##                Df AIC BIC   Chisq Chisq diff Df diff Pr(>Chisq)    
## fit.configural 16          107.42                                  
## fit.loadings   20          168.66      72.16       4  7.956e-15 ***
## fit.intercepts 27          283.62     218.64       7  < 2.2e-16 ***
## fit.means      29         4616.84    1004.10       2  < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Fit measures:
## 
##                cfi.scaled rmsea.scaled cfi.scaled.delta rmsea.scaled.delta
## fit.configural      0.989        0.067               NA                 NA
## fit.loadings        0.985        0.071            0.005              0.004
## fit.intercepts      0.973        0.081            0.012              0.010
## fit.means           0.680        0.269            0.293              0.188

Model test and approximate fit indices

##          chisq.scaled             df.scaled         pvalue.scaled 
##               256.839                33.000                 0.000 
##            cfi.scaled            tli.scaled          rmsea.scaled 
##                 0.978                 0.973                 0.036 
## rmsea.ci.lower.scaled rmsea.ci.upper.scaled                  srmr 
##                 0.033                 0.039                 0.035 
##                  pnfi                   bic 
##                 0.629            144503.285

Main model parameters with BFs

lhs op rhs z pvalue est std.all BF10 Posterior
32 dINTMAT ~ INTMAT6 -15.80 0.00 -0.52 -0.43 3.014559e+53 1.00
31 dINTMAT ~ ACH6 9.10 0.00 0.23 0.24 2.713399e+37 1.00
30 dACH ~ ACH6 6.13 0.00 0.13 0.27 2.202615e+10 1.00
29 dACH ~ INTMAT6 1.12 0.26 0.02 0.04 4.000000e-02 0.04
34 dINTMAT ~~ dACH 10.61 0.00 0.06 0.38 3.815822e+45 1.00
33 INTMAT6 ~~ ACH6 11.19 0.00 0.08 0.25 6.682365e+46 1.00
15 dINTMAT ~1 11.58 0.00 1.12 1.86 NA NA
16 dINTMAT ~~ dINTMAT 19.35 0.00 0.29 0.81 NA NA
23 dACH ~1 6.44 0.00 0.42 1.32 NA NA
24 dACH ~~ dACH 11.55 0.00 0.09 0.90 NA NA
17 INTMAT6 ~1 156.56 0.00 2.79 5.56 NA NA
25 ACH6 ~1 -11.11 0.00 -0.33 -0.50 NA NA

Model parameters per subgroup

Group 1 = ZS, Group 2 = VG

lhs op rhs group est se z std.all group.1 est.1 se.1 z.1 std.all.1
32 dINTMAT ~ INTMAT6 1 -0.545 0.037 -14.660 -0.459 2 -0.442 0.055 -8.026 -0.329
31 dINTMAT ~ ACH6 1 0.300 0.031 9.620 0.291 2 0.340 0.057 5.923 0.239
30 dACH ~ ACH6 1 0.125 0.030 4.144 0.227 2 0.402 0.059 6.803 0.487
29 dACH ~ INTMAT6 1 0.016 0.025 0.640 0.025 2 0.048 0.032 1.507 0.061
34 dINTMAT ~~ dACH 1 0.065 0.007 9.276 0.388 2 0.045 0.010 4.705 0.291
33 INTMAT6 ~~ ACH6 1 0.077 0.007 10.536 0.270 2 0.028 0.007 4.015 0.168
15 dINTMAT ~1 1 1.260 0.111 11.301 2.070 2 0.625 0.166 3.757 1.089
16 dINTMAT ~~ dINTMAT 1 0.286 0.017 17.185 0.773 2 0.284 0.025 11.179 0.863
23 dACH ~1 1 0.451 0.076 5.948 1.389 2 0.190 0.092 2.060 0.571
24 dACH ~~ dACH 1 0.097 0.009 10.316 0.925 2 0.083 0.014 5.901 0.751
17 INTMAT6 ~1 1 2.775 0.020 137.282 5.422 2 2.883 0.024 122.573 6.742
25 ACH6 ~1 1 -0.460 0.025 -18.468 -0.779 2 0.482 0.039 12.236 1.195

Likelihood ratio tests

Tests whether constraining the given parameter across both types of school results in a significantly worse fit (i.e., whether the parameter differs between the groups)

## $`dINTMAT~INTMAT6`
##                 Chisq diff Df diff Pr(>Chisq)
## fit.constrained     2.1951       1     0.1385
## 
## $`dINTMAT~ACH6`
##                 Chisq diff Df diff Pr(>Chisq)
## fit.constrained    0.56526       1     0.4521
## 
## $`dACH~ACH6`
##                 Chisq diff Df diff Pr(>Chisq)    
## fit.constrained     13.107       1  0.0002942 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## $`dACH~INTMAT6`
##                 Chisq diff Df diff Pr(>Chisq)
## fit.constrained    0.63865       1     0.4242
## 
## $`dINTMAT~~dACH`
##                 Chisq diff Df diff Pr(>Chisq)
## fit.constrained     2.2648       1     0.1323
## 
## $`INTMAT6 ~~ ACH6`
##                 Chisq diff Df diff Pr(>Chisq)    
## fit.constrained     19.705       1  9.038e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## $`dINTMAT~1`
##                 Chisq diff Df diff Pr(>Chisq)   
## fit.constrained     9.1924       1    0.00243 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## $`dACH~1`
##                 Chisq diff Df diff Pr(>Chisq)  
## fit.constrained     3.5096       1    0.06101 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

BLCSM for COMLRN

Measurement invariance for COMLRN across grades

Invariance with respect to type of school in 6th grade

## 
## Measurement invariance models:
## 
## Model 1 : fit.configural
## Model 2 : fit.loadings
## Model 3 : fit.intercepts
## Model 4 : fit.means
## 
## Scaled Chi Square Difference Test (method = "satorra.bentler.2001")
## 
##                Df AIC BIC    Chisq Chisq diff Df diff Pr(>Chisq)    
## fit.configural 26           76.526                                  
## fit.loadings   31           98.341      33.09       5  3.607e-06 ***
## fit.intercepts 40          154.786     104.55       9  < 2.2e-16 ***
## fit.means      42         5981.445    1748.07       2  < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Fit measures:
## 
##                cfi.scaled rmsea.scaled cfi.scaled.delta rmsea.scaled.delta
## fit.configural      0.995        0.034               NA                 NA
## fit.loadings        0.994        0.036            0.002              0.002
## fit.intercepts      0.989        0.042            0.005              0.006
## fit.means           0.578        0.256            0.412              0.214

Invariance with respect to type of school in 9th grade

## 
## Measurement invariance models:
## 
## Model 1 : fit.configural
## Model 2 : fit.loadings
## Model 3 : fit.intercepts
## Model 4 : fit.means
## 
## Scaled Chi Square Difference Test (method = "satorra.bentler.2001")
## 
##                Df AIC BIC   Chisq Chisq diff Df diff Pr(>Chisq)    
## fit.configural 26          116.91                                  
## fit.loadings   31          145.21      36.43       5  7.782e-07 ***
## fit.intercepts 40          193.57      85.03       9  1.607e-14 ***
## fit.means      42         4598.87    1216.85       2  < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Fit measures:
## 
##                cfi.scaled rmsea.scaled cfi.scaled.delta rmsea.scaled.delta
## fit.configural      0.993        0.046               NA                 NA
## fit.loadings        0.992        0.047            0.002              0.001
## fit.intercepts      0.988        0.049            0.003              0.002
## fit.means           0.735        0.224            0.253              0.176

Model test and approximate fit indices

##          chisq.scaled             df.scaled         pvalue.scaled 
##               188.414                41.000                 0.000 
##            cfi.scaled            tli.scaled          rmsea.scaled 
##                 0.985                 0.982                 0.026 
## rmsea.ci.lower.scaled rmsea.ci.upper.scaled                  srmr 
##                 0.024                 0.028                 0.022 
##                  pnfi                   bic 
##                 0.694            159154.436

Main model parameters with BFs

lhs op rhs z pvalue est std.all BF10 Posterior
34 dCOMLRN ~ COMLRN6 -28.29 0.00 -0.60 -0.55 2.025977e+149 1.00
33 dCOMLRN ~ ACH6 5.47 0.00 0.12 0.11 6.775458e+08 1.00
32 dACH ~ ACH6 6.14 0.00 0.13 0.27 2.093115e+10 1.00
31 dACH ~ COMLRN6 0.61 0.54 0.01 0.02 2.000000e-02 0.02
36 dCOMLRN ~~ dACH 7.11 0.00 0.05 0.25 4.321580e+18 1.00
35 COMLRN6 ~~ ACH6 2.73 0.01 0.03 0.06 2.152000e+01 0.96
17 dCOMLRN ~1 26.06 0.00 1.61 2.22 NA NA
18 dCOMLRN ~~ dCOMLRN 26.05 0.00 0.36 0.69 NA NA
25 dACH ~1 10.70 0.00 0.47 1.49 NA NA
26 dACH ~~ dACH 11.56 0.00 0.09 0.91 NA NA
19 COMLRN6 ~1 151.29 0.00 2.81 4.19 NA NA
27 ACH6 ~1 -11.11 0.00 -0.33 -0.50 NA NA

Model parameters per subgroup

Group 1 = ZS, Group 2 = VG

lhs op rhs group est se z std.all group.1 est.1 se.1 z.1 std.all.1
34 dCOMLRN ~ COMLRN6 1 -0.599 0.025 -24.284 -0.550 2 -0.619 0.034 -18.071 -0.588
33 dCOMLRN ~ ACH6 1 0.182 0.029 6.369 0.147 2 0.074 0.044 1.674 0.040
32 dACH ~ ACH6 1 0.120 0.030 4.041 0.220 2 0.402 0.060 6.732 0.496
31 dACH ~ COMLRN6 1 0.011 0.016 0.705 0.023 2 -0.019 0.020 -0.939 -0.041
36 dCOMLRN ~~ dACH 1 0.047 0.007 6.378 0.255 2 0.026 0.009 2.902 0.153
35 COMLRN6 ~~ ACH6 1 0.027 0.011 2.511 0.073 2 0.001 0.010 0.088 0.003
17 dCOMLRN ~1 1 1.644 0.071 23.034 2.277 2 1.639 0.103 15.984 2.201
18 dCOMLRN ~~ dCOMLRN 1 0.359 0.016 22.814 0.689 2 0.358 0.021 17.183 0.646
25 dACH ~1 1 0.462 0.052 8.904 1.453 2 0.383 0.067 5.714 1.182
26 dACH ~~ dACH 1 0.094 0.009 10.200 0.931 2 0.079 0.014 5.816 0.755
19 COMLRN6 ~1 1 2.788 0.021 133.706 4.210 2 2.917 0.030 95.739 4.130
27 ACH6 ~1 1 -0.460 0.025 -18.468 -0.788 2 0.482 0.039 12.236 1.206

Likelihood ratio tests

Tests whether constraining the given parameter across both types of school results in a significantly worse fit (i.e., whether the parameter differs between the groups)

## $`dCOMLRN~COMLRN6`
##                 Chisq diff Df diff Pr(>Chisq)
## fit.constrained    0.42006       1     0.5169
## 
## $`dCOMLRN~ACH6`
##                 Chisq diff Df diff Pr(>Chisq)  
## fit.constrained     3.1996       1    0.07365 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## $`dACH~ACH6`
##                 Chisq diff Df diff Pr(>Chisq)    
## fit.constrained     13.287       1  0.0002673 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## $`dACH~COMLRN6`
##                 Chisq diff Df diff Pr(>Chisq)
## fit.constrained     1.3218       1     0.2503
## 
## $`dCOMLRN~~dACH`
##                 Chisq diff Df diff Pr(>Chisq)  
## fit.constrained     2.9179       1     0.0876 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## $`COMLRN6 ~~ ACH6`
##                 Chisq diff Df diff Pr(>Chisq)  
## fit.constrained     2.9913       1    0.08371 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## $`dCOMLRN~1`
##                 Chisq diff Df diff Pr(>Chisq)
## fit.constrained    0.26566       1     0.6063
## 
## $`dACH~1`
##                 Chisq diff Df diff Pr(>Chisq)
## fit.constrained    0.89794       1     0.3433

BLCSM for SCVERB

Measurement invariance for SCVERB across grades

Invariance with respect to type of school in 6th grade

## 
## Measurement invariance models:
## 
## Model 1 : fit.configural
## Model 2 : fit.loadings
## Model 3 : fit.intercepts
## Model 4 : fit.means
## 
## Scaled Chi Square Difference Test (method = "satorra.bentler.2001")
## 
##                Df AIC BIC   Chisq Chisq diff Df diff Pr(>Chisq)    
## fit.configural 16          457.88                                  
## fit.loadings   20          502.55      55.19       4  2.959e-11 ***
## fit.intercepts 27          539.87      63.97       7  2.424e-11 ***
## fit.means      29         6660.77    1971.10       2  < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Fit measures:
## 
##                cfi.scaled rmsea.scaled cfi.scaled.delta rmsea.scaled.delta
## fit.configural      0.952        0.128               NA                 NA
## fit.loadings        0.950        0.117            0.002              0.011
## fit.intercepts      0.944        0.106            0.006              0.011
## fit.means           0.440        0.325            0.505              0.219

Invariance with respect to type of school in 9th grade

## 
## Measurement invariance models:
## 
## Model 1 : fit.configural
## Model 2 : fit.loadings
## Model 3 : fit.intercepts
## Model 4 : fit.means
## 
## Scaled Chi Square Difference Test (method = "satorra.bentler.2001")
## 
##                Df AIC BIC   Chisq Chisq diff Df diff Pr(>Chisq)    
## fit.configural 16          760.06                                  
## fit.loadings   20          787.69      32.54       4  1.485e-06 ***
## fit.intercepts 27          870.45     169.26       7  < 2.2e-16 ***
## fit.means      29         5265.32    1198.30       2  < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Fit measures:
## 
##                cfi.scaled rmsea.scaled cfi.scaled.delta rmsea.scaled.delta
## fit.configural      0.945        0.176               NA                 NA
## fit.loadings        0.948        0.153            0.003              0.023
## fit.intercepts      0.939        0.143            0.009              0.011
## fit.means           0.724        0.293            0.215              0.150

Model test and approximate fit indices

##          chisq.scaled             df.scaled         pvalue.scaled 
##               603.347                32.000                 0.000 
##            cfi.scaled            tli.scaled          rmsea.scaled 
##                 0.943                 0.929                 0.058 
## rmsea.ci.lower.scaled rmsea.ci.upper.scaled                  srmr 
##                 0.056                 0.061                 0.065 
##                  pnfi                   bic 
##                 0.613            134458.776

Main model parameters with BFs

lhs op rhs z pvalue est std.all BF10 Posterior
32 dSCVERB ~ SCVERB6 -20.21 0.00 -0.49 -0.49 2.894246e+84 1.00
31 dSCVERB ~ ACH6 4.83 0.00 0.10 0.11 9.759586e+05 1.00
30 dACH ~ ACH6 6.18 0.00 0.13 0.28 2.701477e+10 1.00
29 dACH ~ SCVERB6 -1.80 0.07 -0.03 -0.06 1.400000e-01 0.12
34 dSCVERB ~~ dACH 2.64 0.01 0.02 0.11 5.019000e+01 0.98
33 SCVERB6 ~~ ACH6 7.83 0.00 0.07 0.20 5.575924e+25 1.00
15 dSCVERB ~1 19.78 0.00 1.38 2.27 NA NA
16 dSCVERB ~~ dSCVERB 23.18 0.00 0.29 0.78 NA NA
23 dACH ~1 11.24 0.00 0.58 1.83 NA NA
24 dACH ~~ dACH 11.54 0.00 0.09 0.91 NA NA
17 SCVERB6 ~1 163.75 0.00 2.77 4.59 NA NA
25 ACH6 ~1 -11.11 0.00 -0.33 -0.50 NA NA

Model parameters per subgroup

Group 1 = ZS, Group 2 = VG

lhs op rhs group est se z std.all group.1 est.1 se.1 z.1 std.all.1
32 dSCVERB ~ SCVERB6 1 -0.499 0.027 -18.683 -0.500 2 -0.475 0.045 -10.482 -0.426
31 dSCVERB ~ ACH6 1 0.157 0.023 6.822 0.153 2 0.006 0.069 0.082 0.003
30 dACH ~ ACH6 1 0.122 0.030 3.993 0.223 2 0.426 0.060 7.115 0.527
29 dACH ~ SCVERB6 1 -0.019 0.019 -0.972 -0.035 2 -0.105 0.031 -3.438 -0.199
34 dSCVERB ~~ dACH 1 0.014 0.008 1.829 0.087 2 0.021 0.010 2.174 0.122
33 SCVERB6 ~~ ACH6 1 0.061 0.009 6.521 0.188 2 0.033 0.011 3.085 0.138
15 dSCVERB ~1 1 1.443 0.076 18.884 2.428 2 1.307 0.139 9.388 1.907
16 dSCVERB ~~ dSCVERB 1 0.269 0.013 20.682 0.763 2 0.385 0.025 15.549 0.818
23 dACH ~1 1 0.544 0.061 8.964 1.720 2 0.624 0.095 6.546 1.926
24 dACH ~~ dACH 1 0.093 0.009 10.142 0.933 2 0.075 0.013 5.724 0.716
17 SCVERB6 ~1 1 2.743 0.019 147.274 4.602 2 2.937 0.029 102.164 4.773
25 ACH6 ~1 1 -0.460 0.025 -18.468 -0.791 2 0.482 0.039 12.236 1.203

Likelihood ratio tests

Tests whether constraining the given parameter across both types of school results in a significantly worse fit (i.e., whether the parameter differs between the groups)

## $`dSCVERB~SCVERB6`
##                 Chisq diff Df diff Pr(>Chisq)
## fit.constrained     0.4237       1     0.5151
## 
## $`dSCVERB~ACH6`
##                 Chisq diff Df diff Pr(>Chisq)  
## fit.constrained     2.9351       1    0.08667 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## $`dACH~ACH6`
##                 Chisq diff Df diff Pr(>Chisq)    
## fit.constrained     15.484       1  8.319e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## $`dACH~SCVERB6`
##                 Chisq diff Df diff Pr(>Chisq)  
## fit.constrained     4.4363       1    0.03518 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## $`dSCVERB~~dACH`
##                 Chisq diff Df diff Pr(>Chisq)
## fit.constrained    0.43069       1     0.5116
## 
## $`SCVERB6 ~~ ACH6`
##                 Chisq diff Df diff Pr(>Chisq)  
## fit.constrained     3.4145       1    0.06463 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## $`dSCVERB~1`
##                 Chisq diff Df diff Pr(>Chisq)
## fit.constrained    0.79919       1     0.3713
## 
## $`dACH~1`
##                 Chisq diff Df diff Pr(>Chisq)
## fit.constrained    0.62858       1     0.4279

BLCSM for SCMATH

Measurement invariance for SCMATH across grades

Invariance with respect to type of school in 6th grade

## 
## Measurement invariance models:
## 
## Model 1 : fit.configural
## Model 2 : fit.loadings
## Model 3 : fit.intercepts
## Model 4 : fit.means
## 
## Scaled Chi Square Difference Test (method = "satorra.bentler.2001")
## 
##                Df AIC BIC   Chisq Chisq diff Df diff Pr(>Chisq)    
## fit.configural 16          324.65                                  
## fit.loadings   20          361.73      48.28       4  8.248e-10 ***
## fit.intercepts 27          488.89     249.01       7  < 2.2e-16 ***
## fit.means      29         6498.01    1822.34       2  < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Fit measures:
## 
##                cfi.scaled rmsea.scaled cfi.scaled.delta rmsea.scaled.delta
## fit.configural      0.973        0.116               NA                 NA
## fit.loadings        0.973        0.105            0.001              0.011
## fit.intercepts      0.961        0.108            0.011              0.002
## fit.means           0.602        0.334            0.360              0.226

Invariance with respect to type of school in 9th grade

## 
## Measurement invariance models:
## 
## Model 1 : fit.configural
## Model 2 : fit.loadings
## Model 3 : fit.intercepts
## Model 4 : fit.means
## 
## Scaled Chi Square Difference Test (method = "satorra.bentler.2001")
## 
##                Df AIC BIC   Chisq Chisq diff Df diff Pr(>Chisq)    
## fit.configural 16          204.97                                  
## fit.loadings   20          264.84      55.62       4  2.413e-11 ***
## fit.intercepts 27          377.38     232.49       7  < 2.2e-16 ***
## fit.means      29         4876.57     911.66       2  < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Fit measures:
## 
##                cfi.scaled rmsea.scaled cfi.scaled.delta rmsea.scaled.delta
## fit.configural      0.984        0.107               NA                 NA
## fit.loadings        0.985        0.094            0.000              0.012
## fit.intercepts      0.978        0.099            0.007              0.004
## fit.means           0.811        0.277            0.167              0.179

Model test and approximate fit indices

##          chisq.scaled             df.scaled         pvalue.scaled 
##               490.715                34.000                 0.000 
##            cfi.scaled            tli.scaled          rmsea.scaled 
##                 0.963                 0.956                 0.051 
## rmsea.ci.lower.scaled rmsea.ci.upper.scaled                  srmr 
##                 0.048                 0.053                 0.049 
##                  pnfi                   bic 
##                 0.623            138822.151

Main model parameters with BFs

lhs op rhs z pvalue est std.all BF10 Posterior
32 dSCMATH ~ SCMATH6 -18.29 0 -0.45 -0.46 3.060891e+88 1.00
31 dSCMATH ~ ACH6 11.90 0 0.36 0.36 6.671553e+64 1.00
30 dACH ~ ACH6 4.90 0 0.11 0.23 8.344668e+05 1.00
29 dACH ~ SCMATH6 3.29 0 0.05 0.11 2.940000e+01 0.97
34 dSCMATH ~~ dACH 10.84 0 0.07 0.40 6.096200e+49 1.00
33 SCMATH6 ~~ ACH6 17.65 0 0.17 0.44 6.339816e+161 1.00
15 dSCMATH ~1 12.50 0 1.06 1.60 NA NA
16 dSCMATH ~~ dSCMATH 25.91 0 0.35 0.81 NA NA
23 dACH ~1 5.60 0 0.32 1.00 NA NA
24 dACH ~~ dACH 11.78 0 0.09 0.89 NA NA
17 SCMATH6 ~1 153.25 0 3.11 4.61 NA NA
25 ACH6 ~1 -11.11 0 -0.33 -0.49 NA NA

Model parameters per subgroup

Group 1 = ZS, Group 2 = VG

lhs op rhs group est se z std.all group.1 est.1 se.1 z.1 std.all.1
32 dSCMATH ~ SCMATH6 1 -0.486 0.027 -17.898 -0.499 2 -0.440 0.049 -8.933 -0.399
31 dSCMATH ~ ACH6 1 0.481 0.036 13.194 0.428 2 0.418 0.073 5.754 0.276
30 dACH ~ ACH6 1 0.105 0.032 3.286 0.191 2 0.377 0.062 6.105 0.453
29 dACH ~ SCMATH6 1 0.042 0.019 2.215 0.088 2 0.079 0.031 2.566 0.130
34 dSCMATH ~~ dACH 1 0.073 0.008 9.180 0.399 2 0.060 0.010 5.778 0.356
33 SCMATH6 ~~ ACH6 1 0.182 0.011 16.580 0.471 2 0.072 0.009 8.334 0.322
15 dSCMATH ~1 1 1.269 0.098 12.980 1.897 2 0.769 0.162 4.748 1.236
16 dSCMATH ~~ dSCMATH 1 0.344 0.015 22.474 0.768 2 0.323 0.024 13.347 0.834
23 dACH ~1 1 0.357 0.069 5.158 1.093 2 0.080 0.097 0.823 0.232
24 dACH ~~ dACH 1 0.098 0.009 10.510 0.919 2 0.087 0.015 6.004 0.742
17 SCMATH6 ~1 1 3.076 0.023 136.471 4.484 2 3.291 0.034 97.613 5.836
25 ACH6 ~1 1 -0.460 0.025 -18.468 -0.773 2 0.482 0.039 12.236 1.172

Likelihood ratio tests

Tests whether constraining the given parameter across both types of school results in a significantly worse fit (i.e., whether the parameter differs between the groups)

## $`dSCMATH~SCMATH6`
##                 Chisq diff Df diff Pr(>Chisq)
## fit.constrained    0.76935       1     0.3804
## 
## $`dSCMATH~ACH6`
##                 Chisq diff Df diff Pr(>Chisq)
## fit.constrained    0.71876       1     0.3966
## 
## $`dACH~ACH6`
##                 Chisq diff Df diff Pr(>Chisq)    
## fit.constrained     11.779       1  0.0005991 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## $`dACH~SCMATH6`
##                 Chisq diff Df diff Pr(>Chisq)
## fit.constrained    0.98997       1     0.3198
## 
## $`dSCMATH~~dACH`
##                 Chisq diff Df diff Pr(>Chisq)
## fit.constrained     1.0232       1     0.3118
## 
## $`SCMATH6 ~~ ACH6`
##                 Chisq diff Df diff Pr(>Chisq)    
## fit.constrained     49.821       1  1.684e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## $`dSCMATH~1`
##                 Chisq diff Df diff Pr(>Chisq)  
## fit.constrained     5.3162       1    0.02113 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## $`dACH~1`
##                 Chisq diff Df diff Pr(>Chisq)  
## fit.constrained     4.0508       1    0.04415 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

BLCSM for SCACAD

Measurement invariance for SCACAD across grades

Invariance with respect to type of school in 6th grade

## 
## Measurement invariance models:
## 
## Model 1 : fit.configural
## Model 2 : fit.loadings
## Model 3 : fit.intercepts
## Model 4 : fit.means
## 
## Scaled Chi Square Difference Test (method = "satorra.bentler.2001")
## 
##                Df AIC BIC    Chisq Chisq diff Df diff Pr(>Chisq)    
## fit.configural 16           85.556                                  
## fit.loadings   20          117.538      44.55       4  4.926e-09 ***
## fit.intercepts 27          134.216      27.13       7  0.0003163 ***
## fit.means      29         6147.908    2489.79       2  < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Fit measures:
## 
##                cfi.scaled rmsea.scaled cfi.scaled.delta rmsea.scaled.delta
## fit.configural      0.992        0.054               NA                 NA
## fit.loadings        0.989        0.056            0.003              0.002
## fit.intercepts      0.987        0.051            0.001              0.005
## fit.means           0.455        0.327            0.532              0.275

Invariance with respect to type of school in 9th grade

## 
## Measurement invariance models:
## 
## Model 1 : fit.configural
## Model 2 : fit.loadings
## Model 3 : fit.intercepts
## Model 4 : fit.means
## 
## Scaled Chi Square Difference Test (method = "satorra.bentler.2001")
## 
##                Df AIC BIC   Chisq Chisq diff Df diff Pr(>Chisq)    
## fit.configural 16          141.29                                  
## fit.loadings   20          173.42      34.29       4  6.508e-07 ***
## fit.intercepts 27          185.20      18.63       7   0.009413 ** 
## fit.means      29         4684.02    1510.63       2  < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Fit measures:
## 
##                cfi.scaled rmsea.scaled cfi.scaled.delta rmsea.scaled.delta
## fit.configural      0.986        0.085               NA                 NA
## fit.loadings        0.986        0.076            0.000              0.009
## fit.intercepts      0.986        0.065            0.000              0.010
## fit.means           0.699        0.289            0.286              0.224

Model test and approximate fit indices

##          chisq.scaled             df.scaled         pvalue.scaled 
##               221.211                34.000                 0.000 
##            cfi.scaled            tli.scaled          rmsea.scaled 
##                 0.982                 0.978                 0.032 
## rmsea.ci.lower.scaled rmsea.ci.upper.scaled                  srmr 
##                 0.030                 0.035                 0.029 
##                  pnfi                   bic 
##                 0.631            123234.360

Main model parameters with BFs

lhs op rhs z pvalue est std.all BF10 Posterior
32 dSCACAD ~ SCACAD6 -24.68 0.00 -0.57 -0.61 1.271376e+123 1.00
31 dSCACAD ~ ACH6 10.40 0.00 0.18 0.24 1.738987e+38 1.00
30 dACH ~ ACH6 5.39 0.00 0.12 0.25 3.666074e+07 1.00
29 dACH ~ SCACAD6 1.75 0.08 0.03 0.06 1.400000e-01 0.12
34 dSCACAD ~~ dACH 8.36 0.00 0.04 0.33 1.351632e+30 1.00
33 SCACAD6 ~~ ACH6 12.16 0.00 0.09 0.30 5.560676e+64 1.00
15 dSCACAD ~1 22.37 0.00 1.67 3.39 NA NA
16 dSCACAD ~~ dSCACAD 22.38 0.00 0.16 0.67 NA NA
23 dACH ~1 5.72 0.00 0.38 1.21 NA NA
24 dACH ~~ dACH 11.44 0.00 0.09 0.91 NA NA
17 SCACAD6 ~1 218.34 0.00 3.04 5.80 NA NA
25 ACH6 ~1 -11.11 0.00 -0.33 -0.50 NA NA

Model parameters per subgroup

Group 1 = ZS, Group 2 = VG

lhs op rhs group est se z std.all group.1 est.1 se.1 z.1 std.all.1
32 dSCACAD ~ SCACAD6 1 -0.594 0.027 -22.376 -0.638 2 -0.561 0.040 -14.167 -0.541
31 dSCACAD ~ ACH6 1 0.253 0.021 12.262 0.297 2 0.162 0.043 3.757 0.142
30 dACH ~ ACH6 1 0.106 0.031 3.400 0.195 2 0.423 0.059 7.166 0.512
29 dACH ~ SCACAD6 1 0.034 0.023 1.497 0.057 2 -0.043 0.043 -1.005 -0.057
34 dSCACAD ~~ dACH 1 0.038 0.005 6.972 0.308 2 0.042 0.006 6.500 0.379
33 SCACAD6 ~~ ACH6 1 0.094 0.008 11.138 0.320 2 0.036 0.008 4.590 0.209
15 dSCACAD ~1 1 1.782 0.086 20.676 3.582 2 1.499 0.121 12.412 3.258
16 dSCACAD ~~ dSCACAD 1 0.158 0.008 19.741 0.638 2 0.150 0.013 11.622 0.708
23 dACH ~1 1 0.384 0.078 4.906 1.210 2 0.454 0.138 3.296 1.364
24 dACH ~~ dACH 1 0.094 0.009 10.114 0.932 2 0.083 0.014 5.782 0.749
17 SCACAD6 ~1 1 3.017 0.016 194.584 5.652 2 3.173 0.021 153.029 7.156
25 ACH6 ~1 1 -0.460 0.025 -18.468 -0.786 2 0.482 0.039 12.236 1.199

Likelihood ratio tests

Tests whether constraining the given parameter across both types of school results in a significantly worse fit (i.e., whether the parameter differs between the groups)

## $`dSCACAD~SCACAD6`
##                 Chisq diff Df diff Pr(>Chisq)
## fit.constrained    0.61952       1     0.4312
## 
## $`dSCACAD~ACH6`
##                 Chisq diff Df diff Pr(>Chisq)
## fit.constrained     2.3862       1     0.1224
## 
## $`dACH~ACH6`
##                 Chisq diff Df diff Pr(>Chisq)    
## fit.constrained     17.074       1  3.596e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## $`dACH~SCACAD6`
##                 Chisq diff Df diff Pr(>Chisq)
## fit.constrained      2.008       1     0.1565
## 
## $`dSCACAD~~dACH`
##                 Chisq diff Df diff Pr(>Chisq)
## fit.constrained     0.4185       1     0.5177
## 
## $`SCACAD6 ~~ ACH6`
##                 Chisq diff Df diff Pr(>Chisq)    
## fit.constrained     22.417       1  2.194e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## $`dSCACAD~1`
##                 Chisq diff Df diff Pr(>Chisq)  
## fit.constrained     3.2734       1    0.07041 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## $`dACH~1`
##                 Chisq diff Df diff Pr(>Chisq)
## fit.constrained    0.44564       1     0.5044

Summary tables

Model test

chisq.scaled df.scaled pvalue.scaled cfi.scaled tli.scaled rmsea.scaled rmsea.ci.lower.scaled rmsea.ci.upper.scaled srmr pnfi bic
sem.fit.INSMOT 230.586 32 0 0.980 0.974 0.034 0.032 0.037 0.033 0.629 138825.7
sem.fit.EFFPER 385.104 44 0 0.967 0.962 0.038 0.036 0.041 0.051 0.684 158722.5
sem.fit.SELFEF 297.768 42 0 0.976 0.972 0.034 0.032 0.036 0.026 0.689 153173.1
sem.fit.CEXP 208.821 43 0 0.983 0.980 0.027 0.025 0.029 0.025 0.693 161384.6
sem.fit.INTREA 263.497 33 0 0.983 0.979 0.036 0.034 0.039 0.045 0.632 143769.9
sem.fit.INTMAT 256.839 33 0 0.978 0.973 0.036 0.033 0.039 0.035 0.629 144503.3
sem.fit.COMLRN 188.414 41 0 0.985 0.982 0.026 0.024 0.028 0.022 0.694 159154.4
sem.fit.SCVERB 603.347 32 0 0.943 0.929 0.058 0.056 0.061 0.065 0.613 134458.8
sem.fit.SCMATH 490.715 34 0 0.963 0.956 0.051 0.048 0.053 0.049 0.623 138822.2
sem.fit.SCACAD 221.211 34 0 0.982 0.978 0.032 0.030 0.035 0.029 0.631 123234.4

Modification indices

## [[1]]
##        lhs op    rhs        mi    epc
## 28    ACH9 ~~   ACH9 37194.460  0.845
## 165 C6_B1H ~~ r9_B1L 20107.711 -1.327
## 183 r9_B1C ~~ r9_B1L 18109.353  0.918
## 153 C6_B1C ~~ C6_B1L 12591.842  0.727
## 191 r9_B1H ~~ r9_B1L  7819.285  0.603
## 
## [[2]]
##         lhs op    rhs        mi    epc
## 30     ACH9 ~~   ACH9 37276.642  0.847
## 275 EFFPER9 ~~   ACH9  7300.386 -0.163
## 264  math_9 ~~ lear_9  3964.607  0.250
## 137 dEFFPER =~ lear_6  3908.331  2.301
## 254  math_6 ~~ lear_9  3776.078 -0.279
## 
## [[3]]
##         lhs op    rhs        mi   epc
## 30     ACH9 ~~   ACH9 35627.555 0.835
## 153    dACH =~ math_9  3947.948 1.154
## 264  math_9 ~~ lear_9  3764.801 0.241
## 88  SELFEF6 =~ math_9  3518.924 0.195
## 99  SELFEF9 =~ math_9  3518.924 0.195
## 
## [[4]]
##        lhs op    rhs        mi    epc
## 30    ACH9 ~~   ACH9 36391.732  0.836
## 264 math_9 ~~ lear_9  3894.269  0.248
## 153   dACH =~ math_9  3760.296  1.133
## 254 math_6 ~~ lear_9  3573.921 -0.268
## 150   dACH =~ math_6  3321.849 -1.078
## 
## [[5]]
##         lhs op     rhs        mi    epc
## 20  INTREA9 ~~ INTREA9 362549.59  4.964
## 164  C6_B2K ~~ r9x_B2E  39373.18 -1.837
## 28     ACH9 ~~    ACH9  37454.76  0.847
## 154  C6_B2E ~~ r9x_B2K  30977.53 -1.393
## 182 r9x_B2E ~~ r9x_B2K  13658.53  0.594
## 
## [[6]]
##         lhs op     rhs         mi     epc
## 165  C6_B2H ~~ r9x_B2Q 196867.874 -12.410
## 28     ACH9 ~~    ACH9  37878.076   0.881
## 191 r9x_B2H ~~ r9x_B2Q  29201.917   1.438
## 163  C6_B2H ~~  C6_B2Q  28307.539   2.195
## 182 r9x_B2A ~~ r9x_B2H   7736.319   0.598
## 
## [[7]]
##         lhs op     rhs        mi    epc
## 30     ACH9 ~~    ACH9 36922.628  0.849
## 186  C6_B2I ~~ r9x_B2C  7451.163 -0.524
## 217 r9x_B2C ~~ r9x_B2I  4250.359  0.324
## 174  C6_B2C ~~ r9x_B2I  4067.121 -0.384
## 264  math_9 ~~  lear_9  3884.164  0.247
## 
## [[8]]
##        lhs op     rhs        mi    epc
## 28    ACH9 ~~    ACH9 37018.823  0.837
## 173 C6_B2R ~~ r9x_B2G 12380.362 -1.130
## 155 C6_B2G ~~ r9x_B2R  5958.657 -0.534
## 219 math_9 ~~  lear_9  4011.423  0.250
## 136   dACH =~  math_9  3778.535  1.135
## 
## [[9]]
##         lhs op     rhs        mi    epc
## 20  SCMATH9 ~~ SCMATH9 469630.00  5.328
## 28     ACH9 ~~    ACH9  37787.12  0.886
## 243 SCMATH9  ~    ACH9  23118.18  3.500
## 246 SCMATH9  ~    ACH6  23118.18  3.500
## 155  C6_B2J ~~ r9x_B2O  16900.05 -0.818
## 
## [[10]]
##        lhs op     rhs        mi    epc
## 28    ACH9 ~~    ACH9 35811.180  0.826
## 219 math_9 ~~  lear_9  3909.642  0.247
## 136   dACH =~  math_9  3804.548  1.137
## 165 C6_B2F ~~ r9x_B2P  3735.115 -0.267
## 67  math_9 ~1          3299.590  0.489

Residuals heatmaps

Overall estimate and posterior

BCSM diagram and parameter values

Pooled sample, undifferentiated by type of school. “##6”, “##9”, “ACH6” and “ACH9” represent the latent measures of non-cognitive SAL constructs and achievement in 6th and 9th grade. “d##” and “dACH” represent the latent change in non-cognitive SAL constructs and achievement accross 6th and 9th grade. In the table, “e..” denotes standardized parameter values, “p..” denotes posterior probability. Labels a-f denote respective parameters.

E.g., talking motivation a consistently negative and pronounced effect of initial motivation on change in motivation. Those with lower initial motivation show greater change (either increase or decrease), those with higher initial motivation are less prone to change markedly. Those with higher initial motivation show higher decrease from 6 to 9. For most SAL domains, this effect is stronger in ZS, but still strong in VG.

d Apart from SCMATH, there is zero effect of initial motivation on change in achievement (controlling for, prior achievement or SES). Ceteris paribus, it is therefore not true that students have to have high initial motivation (or high self-concept) to show larger progress in achievement. Quite stable in ZS for all domains. In VG, there is a possitive effect for SCMATH but a negative one for SCVERB, where VG students with lower motivation show slightly larger shift (mostly loss) in achievement. Likely random fluctuations arround 0.

b On the other hand, those with high initial abilities exhibit greater change in SELFEF, CEXP, SCMATH, SCACAD and slightly also in INTREA, SCVERB, and COMLRN. No effect for INSMOT AND EFFPER. Dynamics in motivation and SC thus seem to be sensitive to whether, at the beginning, we have a high or low performing student. On average (!!!), given the means the trend of shift is rather in negative direction - smarter students (although generally higher on motivation and self-concept) are more sensitive to lose more of it from grade 6 to 9, as compared to less smart students (this statement is only valid for domains with pronounced general decline in SAL domains. In domains with less decline, some smart students gain in motivation and SC, some loose.)

c Those with low initial ability on average progress more, those with high initial ability progress less. The estimate is stable, whatever SAL construct is included in the model (indication of no confounding by SAL domains). The effect is rather small for ZS (~.2), but quite big for VG (~.5).

f Initial levels of motivation and ach correlate positively for most domains in ZS, not so much in VG

e There is an association between the rate of change in the studied domains. I.e., the degrees of changes co-occur after taking into account the coupling pathways. This relationship is explained by achievement, but not by motivation or SC.

Parameter Label eINSMOT stdINSMOT pINSMOT eEFFPER stdEFFPER pEFFPER eSELFEF stdSELFEF pSELFEF eCEXP stdCEXP pCEXP eINTREA stdINTREA pINTREA eINTMAT stdINTMAT pINTMAT eCOMLRN stdCOMLRN pCOMLRN eSCVERB stdSCVERB pSCVERB eSCMATH stdSCMATH pSCMATH eSCACAD stdSCACAD pSCACAD Label Parameter
32 dX~X6 a -0.58 -0.47 1.00 -0.62 -0.59 1.00 -0.57 -0.59 1.00 -0.51 -0.48 1.00 -0.38 -0.38 1.00 -0.52 -0.43 1.00 -0.60 -0.55 1.00 -0.49 -0.49 1.00 -0.45 -0.46 1.00 -0.57 -0.61 1.00 a dX~X6
31 dX~ACH6 b 0.06 0.06 0.85 0.03 0.03 0.09 0.24 0.31 1.00 0.18 0.19 1.00 0.15 0.11 1.00 0.23 0.24 1.00 0.12 0.11 1.00 0.10 0.11 1.00 0.36 0.36 1.00 0.18 0.24 1.00 b dX~ACH6
30 dACH~ACH6 c 0.13 0.26 1.00 0.13 0.26 1.00 0.13 0.26 1.00 0.13 0.26 1.00 0.13 0.26 1.00 0.13 0.27 1.00 0.13 0.27 1.00 0.13 0.28 1.00 0.11 0.23 1.00 0.12 0.25 1.00 c dACH~ACH6
29 dACH~X6 d 0.03 0.06 0.17 0.01 0.03 0.02 0.03 0.04 0.04 0.01 0.02 0.02 -0.01 -0.02 0.02 0.02 0.04 0.04 0.01 0.02 0.02 -0.03 -0.06 0.12 0.05 0.11 0.97 0.03 0.06 0.12 d dACH~X6
34 dX~~dACH e 0.04 0.25 1.00 0.04 0.27 1.00 0.04 0.34 1.00 0.05 0.29 1.00 0.03 0.12 1.00 0.06 0.38 1.00 0.05 0.25 1.00 0.02 0.11 0.98 0.07 0.40 1.00 0.04 0.33 1.00 e dX~~dACH
33 X6~~ACH6 f 0.03 0.10 1.00 0.04 0.11 1.00 0.09 0.32 1.00 0.06 0.17 1.00 0.05 0.09 1.00 0.08 0.25 1.00 0.03 0.06 0.96 0.07 0.20 1.00 0.17 0.44 1.00 0.09 0.30 1.00 f X6~~ACH6

Estimates by type of school

Parameter Label INSMOT_ZS INSMOT_VG LRT.INSMOT EFFPER_ZS EFFPER_VG LRT.EFFPER SELFEF_ZS SELFEF_VG LRT.SELFEF CEXP_ZS CEXP_VG LRT.CEXP INTREA_ZS INTREA_VG LRT.INTREA INTMAT_ZS INTMAT_VG LRT.INTMAT COMLRN_ZS COMLRN_VG LRT.COMLRN SCVERB_ZS SCVERB_VG LRT.SCVERB SCMATH_ZS SCMATH_VG LRT.SCMATH SCACAD_ZS SCACAD_VG LRT.SCACAD Label Parameter
32 dX~X6 a -0.588 -0.561 0.508 -0.637 -0.518 0.018 -0.577 -0.642 0.230 -0.531 -0.438 0.137 -0.383 -0.354 0.419 -0.545 -0.442 0.138 -0.599 -0.619 0.517 -0.499 -0.475 0.515 -0.486 -0.440 0.380 -0.594 -0.561 0.431 a dX~X6
31 dX~ACH6 b 0.105 -0.152 0.000 0.071 -0.125 0.004 0.298 0.223 0.215 0.244 0.096 0.046 0.139 0.051 0.314 0.300 0.340 0.452 0.182 0.074 0.074 0.157 0.006 0.087 0.481 0.418 0.397 0.253 0.162 0.122 b dX~ACH6
30 dACH~ACH6 c 0.114 0.403 0.000 0.119 0.401 0.000 0.116 0.426 0.000 0.117 0.406 0.000 0.118 0.408 0.000 0.125 0.402 0.000 0.120 0.402 0.000 0.122 0.426 0.000 0.105 0.377 0.001 0.106 0.423 0.000 c dACH~ACH6
29 dACH~X6 d 0.034 0.007 0.389 0.010 0.006 0.604 0.032 -0.056 0.091 0.009 -0.023 0.411 0.000 -0.028 0.294 0.016 0.048 0.424 0.011 -0.019 0.250 -0.019 -0.105 0.035 0.042 0.079 0.320 0.034 -0.043 0.156 d dACH~X6
34 dX~~dACH e 0.045 0.023 0.093 0.042 0.007 0.003 0.042 0.029 0.252 0.046 0.034 0.321 0.034 -0.001 0.033 0.065 0.045 0.132 0.047 0.026 0.088 0.014 0.021 0.512 0.073 0.060 0.312 0.038 0.042 0.518 e dX~~dACH
33 X6~~ACH6 f 0.034 -0.011 0.000 0.042 -0.013 0.000 0.091 0.044 0.000 0.061 0.011 0.000 0.024 0.058 0.061 0.077 0.028 0.000 0.027 0.001 0.084 0.061 0.033 0.065 0.182 0.072 0.000 0.094 0.036 0.000 f X6~~ACH6

Conditional means and variances by type of school

Parameter INSMOT_ZS INSMOT_VG EFFPER_ZS EFFPER_VG SELFEF_ZS SELFEF_VG CEXP_ZS CEXP_VG INTREA_ZS INTREA_VG INTMAT_ZS INTMAT_VG COMLRN_ZS COMLRN_VG SCVERB_ZS SCVERB_VG SCMATH_ZS SCMATH_VG SCACAD_ZS SCACAD_VG Parameter
15 dNCC~1 1.725 1.670 1.520 1.068 1.567 1.667 1.540 1.174 0.728 0.793 1.260 0.625 1.644 1.639 1.443 1.307 1.269 0.769 1.782 1.499 dNCC~1
16 dNCC~~dNCC 0.320 0.349 0.219 0.289 0.157 0.192 0.274 0.307 0.646 0.659 0.286 0.284 0.359 0.358 0.269 0.385 0.344 0.323 0.158 0.150 dNCC~~dNCC
23 dACH~1 0.377 0.304 0.463 0.309 0.412 0.469 0.467 0.396 0.492 0.410 0.451 0.190 0.462 0.383 0.544 0.624 0.357 0.080 0.384 0.454 dACH~1
24 dACH~~dACH 0.093 0.079 0.093 0.079 0.095 0.081 0.093 0.080 0.094 0.078 0.097 0.083 0.094 0.079 0.093 0.075 0.098 0.087 0.094 0.083 dACH~~dACH
17 NCC6~1 3.325 3.460 2.978 2.945 2.479 2.732 2.921 3.119 2.750 3.094 2.775 2.883 2.788 2.917 2.743 2.937 3.076 3.291 3.017 3.173 NCC6~1
25 ACH6~1 -0.460 0.482 -0.460 0.482 -0.460 0.482 -0.460 0.482 -0.460 0.482 -0.460 0.482 -0.460 0.482 -0.460 0.482 -0.460 0.482 -0.460 0.482 ACH6~1

Likelihood ratio test for the difference in rate of change

Parameter INSMOT_ZS INSMOT_VG LRT.INSMOT EFFPER_ZS EFFPER_VG LRT.EFFPER SELFEF_ZS SELFEF_VG LRT.SELFEF CEXP_ZS CEXP_VG LRT.CEXP INTREA_ZS INTREA_VG LRT.INTREA INTMAT_ZS INTMAT_VG LRT.INTMAT COMLRN_ZS COMLRN_VG LRT.COMLRN SCVERB_ZS SCVERB_VG LRT.SCVERB SCMATH_ZS SCMATH_VG LRT.SCMATH SCACAD_ZS SCACAD_VG LRT.SCACAD Parameter
15 dNCC~1 1.725 1.670 0.566 1.520 1.068 0.005 1.567 1.667 0.412 1.540 1.174 0.067 0.728 0.793 0.506 1.260 0.625 0.002 1.644 1.639 0.606 1.443 1.307 0.371 1.269 0.769 0.021 1.782 1.499 0.070 dNCC~1
23 dACH~1 0.377 0.304 0.487 0.463 0.309 0.230 0.412 0.469 0.511 0.467 0.396 0.475 0.492 0.410 0.333 0.451 0.190 0.061 0.462 0.383 0.343 0.544 0.624 0.428 0.357 0.080 0.044 0.384 0.454 0.504 dACH~1