`sim_lvm`

can simulate data based on factor analysis or
item response models with different response formats (continuous or categorical),
loading patterns and residual covariance (local dependence) structures.

## Usage

```
sim_lvm(
N = 1000,
mla = NULL,
K = 3,
J = 18,
cpf = 0,
lam = 0.7,
lac = 0.3,
phi = 0.3,
ph12 = -1,
ecr = 0,
P = 0,
b = 0.3,
K1 = 0,
ph1 = 0.2,
b1 = 0.3,
ilvl = NULL,
cati = NULL,
noc = c(4),
misp = 0,
ome_out = FALSE,
necw = K,
necb = K,
add_ind = c(),
add_la = 0.5,
add_phi = 0,
zero_it = 0,
rseed = 333,
digits = 4
)
```

## Arguments

- N
Sample size.

- mla
Population loading matrix.

- K
Number of factors (if

`mla=NULL`

).- J
Number of items (if

`mla=NULL`

).- cpf
Number of cross-loadings per factor (if

`mla=NULL`

).- lam
Number of formal iterations for posterior sampling.

- lac
Number of iterations to update the sampling information.

- phi
Homogeneous correlations between any two factors.

- ph12
Correlation between factor 1 and 2 (if it's different from

`phi`

.- ecr
Residual correlation (local dependence).

- P
Number of observable predictors (for MIMIC model).

- b
Coefficients of observable predictors (for MIMIC model).

- K1
Number of latent predictors (for MIMIC model).

- ph1
Correlations between latent predictors (for MIMIC model).

- b1
Coefficients of latent predictors (for MIMIC model).

- ilvl
Specified levels of all items (i.e., need to specify Item 1 to \(J+P\)); Any value smaller than 2 is considered as continuous item.

- cati
The set of polytomous items in sequence number (i.e., can be any number set in between 1 and \(J+P\));

`NULL`

for no and -1 for all (if`ilvl=NULL`

).- noc
Number of levels for polytomous items.

- misp
Proportion of missingness.

- ome_out
Output factor score or not.

- necw
Number of within-factor local dependence.

- necb
Number of between-factor local dependence.

- add_ind
(Additional) minor factor with cross-loadings.

- add_la
Value of cross-loadings on (Additional) minor factor.

- add_phi
Correlations between (Additional) minor factor and other factors.

- zero_it
Surplus items with zero loading.

- rseed
An integer for the random seed.

- digits
Number of significant digits to print when printing numeric values.

## Examples

```
# for continuous data with cross-loadings and local dependence effect .3
out <- sim_lvm(N=1000,K=3,ipf=6,lam = .7, lac=.3,ecr=.3)
#> Error in sim_lvm(N = 1000, K = 3, ipf = 6, lam = 0.7, lac = 0.3, ecr = 0.3): unused argument (ipf = 6)
summary(out$dat)
#> Error in summary(out$dat): object 'out' not found
out$MLA
#> Error in eval(expr, envir, enclos): object 'out' not found
out$ofd_ind
#> Error in eval(expr, envir, enclos): object 'out' not found
# for categorical data with cross-loadings .4 and 10% missingness
out <- sim_lvm(N=1000,K=3,ipf=6,lam = .7, lac=.4,cati=-1,noc=4,misp=.1)
#> Error in sim_lvm(N = 1000, K = 3, ipf = 6, lam = 0.7, lac = 0.4, cati = -1, noc = 4, misp = 0.1): unused argument (ipf = 6)
summary(out$dat)
#> Error in summary(out$dat): object 'out' not found
out$MLA
#> Error in eval(expr, envir, enclos): object 'out' not found
out$ofd_ind
#> Error in eval(expr, envir, enclos): object 'out' not found
```