mnlfa.RdGeneral function for conducting moderated nonlinear factor analysis (Curran et al., 2014). Item slopes and item intercepts can be modeled as functions of person covariates.
Parameter regularization is allowed. For categorical covariates, group lasso can be used for regularization.
mnlfa(dat, items, item_type="2PL", formula_int=~1, formula_slo=~1, formula_mean=~0, formula_sd=~0, theta=NULL, parm_list_init=NULL, parm_trait_init=NULL, prior_init=NULL, regular_lam=c(0, 0), regular_type=c("none", "none"), maxit=1000, msteps=4, conv=1e-05, conv_mstep=1e-04, h=1e-04, parms_regular_types=NULL, parms_regular_lam=NULL, parms_iterations=NULL, center_parms=NULL, center_max_iter=6, L_max=.07, verbose=TRUE) # S3 method for mnlfa summary(object, file=NULL, ...)
| dat | Data frame with item responses |
|---|---|
| items | Vector containing item names |
| item_type | String or vector of item types. Currently, only item types |
| formula_int | String or list with formula for item intercepts |
| formula_slo | String or list with formula for item slopes |
| formula_mean | Formula for mean of the trait distribution |
| formula_sd | Formula for standard deviation of the trait distribution |
| theta | Grid of \(\theta\) values used for approximation of normally distributed trait |
| parm_list_init | Optional list of initial item parameters |
| parm_trait_init | Optional list of initial parameters for trait distribution |
| prior_init | Optional matrix of prior distribution for persons |
| regular_lam | Vector of length two containing two general regularization parameters for item intercepts and item slopes |
| regular_type | Type of regularization method. Can be |
| maxit | Maximum number of iterations |
| msteps | Maximum number of M-steps |
| conv | Convergence criterion with respect to parameters |
| conv_mstep | Convergence criterion in M-step |
| h | Numerical differentiation parameter |
| parms_regular_types | Optional list containing parameter specific regularization types |
| parms_regular_lam | Optional list containing parameter specific regularization parameters |
| parms_iterations | Optional list containing sequence of parameter indices used for updating |
| center_parms | Optional list indicating which parameters should be centered during initial iterations. |
| center_max_iter | Maximum number of iterations in which parameters should be centered. |
| L_max | Majorization parameter used in regularization |
| verbose | Logical indicating whether output should be printed |
| object | Object of class |
| file | Optional file name |
| ... | Further arguments to be passed |
The moderated factor analysis model for dichotomous responses defined as
$$P(X_{pi}=1 | \theta_p )=invlogit( a_{pi} \theta_p - b_{pi} ) $$
The trait distribution \(\theta_p \sim N( \mu_p, \sigma_p^2)\)
allows a latent regression of person covariates on the mean
with \(\mu_p=\bold{X}_p \bold{\gamma}\) (to be specified in formula_mean)
and the logarithm of the standard deviation \(\log \sigma_p=\bold{Z}_p \bold{\delta} \)
(to be specified in formula_sd).
Item intercepts and item slopes can be moderated by person covariates, i.e.
\(a_{pi}=\bold{W}_{pi} \bold{\alpha}_i \) and
\(b_{pi}=\bold{V}_{pi} \bold{\beta}_i \). Regularization on (some of) the
\(\bold{\alpha}_i\) or \(\bold{\beta}_i\) parameters is allowed.
The model is estimated using an EM algorithm with the coordinate descent method during the M-step (Sun et al., 2016).
List with model results including
Summary table for item parameters
Summary table for trait parameters
Curran, P. J., McGinley, J. S., Bauer, D. J., Hussong, A. M., Burns, A., Chassin, L., Sher, K., & Zucker, R. (2014). A moderated nonlinear factor model for the development of commensurate measures in integrative data analysis. Multivariate Behavioral Research, 49(3), 214-231. http://dx.doi.org/10.1080/00273171.2014.889594
Sun, J., Chen, Y., Liu, J., Ying, Z., & Xin, T. (2016). Latent variable selection for multidimensional item response theory models via L1 regularization. Psychometrika, 81(4), 921-939. https://doi.org/10.1007/s11336-016-9529-6
See also the aMNLFA package for automatized moderated nonlinear factor analysis which provides convenient wrapper functions for automized analysis in the Mplus software.
See the GPCMlasso package for the regularized generalized partial credit model.
############################################################################# # EXAMPLE 1: Dichotomous data, 1PL model ############################################################################# data(data.mnlfa01, package="mnlfa") dat <- data.mnlfa01 # extract items from dataset items <- grep("I[0-9]", colnames(dat), value=TRUE) I <- length(items) # maximum number of iterations (use only few iterations for the only purpose of # providing CRAN checks) maxit <- 10 #***** Model 1: 1PL model without moderating parameters and without covariates for traits # no covariates for trait formula_mean <- ~0 formula_sd <- ~1 # no item covariates formula_int <- ~1 formula_slo <- ~1 mod1 <- mnlfa::mnlfa( dat=dat, items, item_type="1PL", formula_int=formula_int, formula_slo=formula_slo, formula_mean=formula_mean, formula_sd=formula_sd, maxit=maxit ) summary(mod1) # \donttest{ #***** Model 2: 1PL model without moderating parameters and with covariates for traits # covariates for trait formula_mean <- ~female + age formula_sd <- ~1 mod2 <- mnlfa::mnlfa( dat=dat, items, item_type="1PL", formula_int=formula_int, formula_slo=formula_slo, formula_mean=formula_mean, formula_sd=formula_sd) summary(mod2) #***** Model 3: 1PL model with moderating parameters and with covariates for traits #*** Regularization method 'mcp' # covariates for trait formula_mean <- ~female + age formula_sd <- ~1 # moderation effects for items formula_int <- ~1+female+age formula_slo <- ~1 # center parameters for female and age in initial iterations for improving convergence center_parms <- list( rep(2,I), rep(3,I) ) # regularization parameters for item intercept and item slope, respectively regular_lam <- c(.06, .25) regular_type <- c("mcp","none") mod3 <- mnlfa::mnlfa( dat=dat, items, item_type="1PL", formula_int=formula_int, formula_slo=formula_slo, formula_mean=formula_mean, formula_sd=formula_sd, center_parms=center_parms, regular_lam=regular_lam, regular_type=regular_type ) summary(mod3) #***** Model 4: 1PL model with selected moderated item parameters #* trait distribution formula_mean <- ~0+female+age formula_sd <- ~1 #* formulas for item intercepts formula_int <- ~1 formula_int <- mnlfa::mnlfa_expand_to_list(x=formula_int, names_list=items) mod_items <- c(4,5,6,7) for (ii in mod_items){ formula_int[[ii]] <- ~1+female+age } formula_slo <- ~1 mod4 <- mnlfa::mnlfa( dat=dat, items, item_type="1PL", formula_int=formula_int, formula_slo=formula_slo, formula_mean=formula_mean, formula_sd=formula_sd) mod4$item mod4$trait summary(mod4) # }