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Applied Analysis Notes

These notes address applied data analysis challenges using Mplus. Mplus is a powerful modeling software package, but has extremely limited data management capabilities. We use Stata and R for our general data analysis and management tasks. Many examples include use our integration of Mplus within the Stata environment.

Note 1: Computing model-implied or expected scores in a growth modeling context from SAVEDATA/FSCORES. 
Latent growth curve model, Mplus, Stata, runmplus, savedata, runmplus_load_savedata, fscores, predicted values, model-implied values, centering, ado, example, simulation

Note 2: Computing model-implied or expected scores from parameter estimates. (coming soon)
Model-implied values, centering, example, simulation

Note 3: Getting factor scores using a fixed set of parameter estimates.
Factor analysis, factor scores, item response theory, runmplus, savedata, fscores, runmplus_load_savedata, Mplus, Stata
Parameter estimates, latent growth model, runmplus, LaTeX, Mplus, Stata

My favorite measure of fit and rules of thumb for judging good fit

After running a latent variable model with covariates, use the r2 from the STANDARDIZED part of the output to re-calibrate the latent variable variance to 1 by constraining the residual variance to 1-r2. This results in more easily interpretable effects of covariates, makes converting to IRT parameter estimates easier (see Macintosh & Hashim 2003), and makes quicky generating plots using canned functions for theoretical standard normal distributions for the latent variable.

Note 7: Draw an Item Characteristic Curve "by hand" using Stata
The easiest way to draw IRT plots is to convert the Mplus parameters to the two parameter logistic (2PL) metric, and then using a function plotting procedure. It is easy to find formulae for the 2PL metric for a variety of IRT functions, including item characteristic curves, item information functions, etc. Click here for code for generating ICCs using both binary and categorical items.

Note 8: Draw an Item Characteristic Curve "by hand" using R
The easiest way to draw IRT plots is to convert the Mplus parameters to the two parameter logistic (2PL) metric, and then using a function plotting procedure. It is easy to find formulae for the 2PL metric for a variety of IRT functions, including item characteristic curves, item information functions, etc. This R notebook covers using R to run Mplus (mplusAutomation::mplusModeler), extracting parameter estimates and savedata from Mplus, and plotting using ggplot2 ICCs. Only the binary test items case is covered.

From Natalia Gouskova