Dear sir:

At first for MIRT you could benefit from this valuable article:

" Item Parameter Estimation for Multidimensional Measurement: Comparisons of SEM and MIRT Based Methods"

By: LIU Hong-Yun;LUO Fang;WANG Yue; ZHANG Yu.

Abstract:

Traditional factor analysis models and estimation methods for continuous (i.e., interval or ratio scale) data are not appropriate for item-level data that are categorical in nature. The authors provide a brief review and synthesis of the item factor analysis estimation literature for categorical data (e.g., 0-1 type response scales) under the multidimensional response model. Popular categorical item factor analysis models and estimation methods found in the structural equation modeling and item response theory literatures are presented.

The Monte Carlo simulation studies are conducted and revealed: (1) Similar parameter estimates have been obtained of Modified weighted least squares for categorical data method (WLSMV) from the structural equation model (SEM) framework and adoptive Restricted Maximum Likelihood (MLR) and Markov chain Monte Carlo (MCMC) methods from the multidimensional item response theory (MIRT) framework. Even with a small sample and the item response theory (IRT) estimates converted to SEM parameters, the WLSMV, MLR, and MCMC results are strikingly similar. But in small sample size and long test, weighted least squares for categorical data (WLSc) did not obtain the convergence parameter estimations, although in short test, WLSc estimates have been obtained, the estimates are consistently more discrepant than those produced by the other estimation techniques. (2) The precision of the estimators enhances as the quantity of the sample increases, and the differences between WLSMV and MLR are very trivial, and the precisions of WLSMV and MLR methods are not worse than that of the MCMC method in most conditions. (3) The precision of item factor loading and of item difficulty parameter is influenced by the test length, and the precision of item discrimination and of item difficulty parameter is influenced by the number of test dimension. (4) The precision of the estimators decreases as the number of dimensions measured by the item increases, especially for item discrimination and item factor loading parameter.

Both SEM and IRT can be used for factor analysis of dichotomous item responses. In this case, the measurement models of both approaches are formally equivalent. They were refined within and across different disciplines, and make complementary contributions to central measurement problems encountered in almost all empirical social science research fields. The authors conclude with considerations for categorical item factor analysis and give some advice for applied researchers.

http://journal.psych.ac.cn/acps/EN/abstract/abstract2225.shtml.

Then for lavaan, you could benefit from this valuable information. As you know:

Estimators-Lavaan principles......

If all data is continuous, the default estimator in the lavaan package is maximum likelihood (estimator = "ML"). Alternative estimators available in lavaan are:

--"GLS": generalized least squares. For complete data only.

-- "WLS": weighted least squares (sometimes called ADF estimation). For complete data only.

-- "DWLS": diagonally weighted least squares.

-- "ULS": unweighted least squares

-- "DLS": distributionally-weighted least squares.

-- "PML": pairwise maximum likelihood

Many estimators have ‘robust’ variants, meaning that they provide robust standard errors and a scaled test statistic. For example, for the maximum likelihood estimator, lavaan provides the following robust variants:

-- "MLM": maximum likelihood estimation with robust standard errors and a Satorra-Bentler scaled test statistic. For complete data only.

-- "MLMVS": maximum likelihood estimation with robust standard errors and a mean- and variance adjusted test statistic (aka the Satterthwaite approach). For complete data only.

-- "MLMV": maximum likelihood estimation with robust standard errors and a mean- and variance adjusted test statistic (using a scale-shifted approach). For complete data only.

-- "MLF": for maximum likelihood estimation with standard errors based on the first-order derivatives, and a conventional test statistic. For both complete and incomplete data.

-- "MLR": maximum likelihood estimation with robust (Huber-White) standard errors and a scaled test statistic that is (asymptotically) equal to the Yuan-Bentler test statistic. For both complete and incomplete data.

Finally for the DWLS and ULS estimators, lavaan also provides ‘robust’ variants: WLSM, WLSMVS, WLSMV, ULSM, ULSMVS, ULSMV. Note that for the robust WLS variants, we use the diagonal of the weight matrix for estimation, but we use the full weight matrix to correct the standard errors and to compute the test statistic.

I hope it will be helpful...

With my best regards

Dear Hassan,

thank your for your feedback. I appreciatted your suggestions.

However, my question focuses only on the factor scores estimators.

All factor scores estimators in mirt and lavaan seems not to work properly. I have performed many analyzes and I found that thefactor scores estimators in lavaan and mirt generate correlations among the factor scores very different in comparison to the correlations among the latent variables of the models (this occurs both in irt models and confirmatory models). However, the ten Berge factor scores estimation in the psych R package worked very well in my analyzes.

Hope I have better explained my question. If you enjoyed my question, observe in your data whether the factor scores in irt or confirmatory factor models will reproduce the correlations of the latent variables in models with two or more latent variables. I believe that the correlations among the latent variables of the models and the correlations among the factor scores will be considerably different, unless you use the ten Berge factor scores estimation.

Best regards,

Cristiano.