APIM Exercise

setwd(mypath)

dat <- read.table("APIM_exercise_data.txt", sep = "\t", header = F)
colnames(dat) <- c("momperc1", "momperc2", "kidach1", "kidach2")

apim_mod <- '
  momperc2 ~ a1*momperc1 + p21*kidach1
  kidach2 ~ a2*kidach1 + p12*momperc1
  momperc1 ~~ kidach1
  momperc2 ~~ kidach2
  
# MODEL CONSTRAINTS

 a1a2 := a1 - a2
 p12p21 := p12 - p21
 a1p21 := a1 - p21
 a2p12 := a2 - p12
 a1p12 := a1 - p12
 a2p21 := a2 - p21


'

apim_fit <- sem(apim_mod, data = dat)
summary(apim_fit, fit.measures = T, standardized = T)

## lavaan 0.6.15 ended normally after 36 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        10
## 
##   Number of observations                           170
## 
## Model Test User Model:
##                                                       
##   Test statistic                                 0.000
##   Degrees of freedom                                 0
## 
## Model Test Baseline Model:
## 
##   Test statistic                               347.312
##   Degrees of freedom                                 6
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    1.000
##   Tucker-Lewis Index (TLI)                       1.000
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)              -1902.349
##   Loglikelihood unrestricted model (H1)      -1902.349
##                                                       
##   Akaike (AIC)                                3824.697
##   Bayesian (BIC)                              3856.055
##   Sample-size adjusted Bayesian (SABIC)       3824.392
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.000
##   90 Percent confidence interval - lower         0.000
##   90 Percent confidence interval - upper         0.000
##   P-value H_0: RMSEA <= 0.050                       NA
##   P-value H_0: RMSEA >= 0.080                       NA
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.000
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Expected
##   Information saturated (h1) model          Structured
## 
## Regressions:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   momperc2 ~                                                            
##     momperc1  (a1)    0.569    0.058    9.887    0.000    0.569    0.622
##     kidach1  (p21)    0.223    0.083    2.700    0.007    0.223    0.170
##   kidach2 ~                                                             
##     kidach1   (a2)    0.550    0.054   10.097    0.000    0.550    0.602
##     momperc1 (p12)    0.154    0.038    4.040    0.000    0.154    0.241
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   momperc1 ~~                                                           
##     kidach1          15.818    2.514    6.292    0.000   15.818    0.551
##  .momperc2 ~~                                                           
##    .kidach2           2.484    0.839    2.960    0.003    2.484    0.233
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .momperc2         16.133    1.750    9.220    0.000   16.133    0.468
##    .kidach2           7.038    0.763    9.220    0.000    7.038    0.420
##     momperc1         41.176    4.466    9.220    0.000   41.176    1.000
##     kidach1          20.018    2.171    9.220    0.000   20.018    1.000
## 
## Defined Parameters:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     a1a2              0.019    0.084    0.220    0.826    0.019    0.020
##     p12p21           -0.069    0.095   -0.728    0.467   -0.069    0.071
##     a1p21             0.346    0.124    2.793    0.005    0.346    0.452
##     a2p12             0.397    0.082    4.849    0.000    0.397    0.361
##     a1p12             0.415    0.061    6.796    0.000    0.415    0.381
##     a2p21             0.327    0.088    3.736    0.000    0.327    0.432