##standardized assessments measurement model 
```{r}

standardized_assessment_cfa <- '
              pre_ol =~ WJIV_Pre_OrlLang_SS + PELI_Pre_VOL_Score + PELI_Pre_COMP_Score
              pre_decode =~ WJIV_Pre_PhnCod_SS + PELI_Pre_AK_Score + PELI_Pre_PA_Score
              
              pre_ol ~~ pre_decode
'

```

### Set Priors 
```{r}

priors <- list(
  nu = "normal(0, 5)",       # intercepts
  lambda = "normal(0.1, 2)", # loadings
  theta = "gamma(1, 1)",     # observed variable precision
  psi = "gamma(1, 1)",       # latent variable precision
  rho = "uniform(-1, 1)"     # latent variable correlation
)


# Set the seed value, for replicability and due to issues with multidimensionality
set.seed(123) # set same seed as was used with simulated data

```

### Features of MCMC

- the number of chains
- the number of iterations to warmup
- the total number of iterations 

```{r MCMC setup}

n.chains = 4
n.warmup = 100
n.burnin = 0
n.iters.per.chain.after.warmup.and.burnin = 1000
n.iters.total.per.chain = n.warmup+n.burnin+n.iters.per.chain.after.warmup.and.burnin

```

###Run Standardized Assessments Measurement Model 

```{r Combined Model}

standardized.measurement.cfa <- bcfa(
  model = standardized_assessment_cfa, # Specify the model
  data = stand.TELL.complete_scaled,   # Specify the data
  dp = priors,                     # Specify priors; ensure 'priors' is correctly defined
  n.chains = n.chains,                   # Set the number of chains
  burnin = n.warmup,                   # Burn-in period; 'burnin' is synonymous with 'warmup' in some contexts
  target = "stan",
  sample = n.iters.per.chain.after.warmup.and.burnin, # Number of iterations after warm-up/burn-in
  mcmcfile = TRUE,                     # Whether to write MCMC model to file
  save.lvs = FALSE,                    # Whether to save latent variable scores
  inits = "simple",                    # Initialization method
  bcontrol = list(cores = n.chains)    # Parallelization control, using multiple cores
)

```