I am running a measurement model with continuous and categorical indicators. However, the standardized results section is only providing the first column (only the estimate and not the SE, Est/SE, and pvalue). Why is this happening?
They will not be exactly the same but should be close.
Marco posted on Saturday, March 03, 2012 - 8:33 am
Hi, Could you please tell me exactly how the standardised loadings are calculated for binary variables in a one-factor model in MPLUS? I'm basically running an IRT model with one factor and I understand the relationship between IRT discrimination and Item Factor Analysis loadings. However I'm less clear about how MPLUS standardises the loadings.
I remember reading somewhere that the standardised loadings are = unstd. loading * SD(Theta) / SD(y)
However, I'm not sure where to get SD(y)in MPLUS or whether this formula is valid for binary indicators.I'm also getting different standardised estimates in other software which returns the same unstandardised estimates as MPLUS.
So basically I have two questions: 1) What is the full loading standardisation formula used by MPLUS for binary variables? 2) Where would one get all the figures used for the standardisation in the MPLUS output (assuming that these are contained in OUTPUT TECH10 and STDYX)?
1. See Techncical Appendix 3 on the website. The variance of an indicator is equal to lamba squared times the variance of the factor plus the residual variance of the factor indicator. The residual variance is one for probit and pi squared divided by 3 for logistic.
2. The factor loadings are found in the results. The factor variance can be found in the results for an unconditional model and TECH4 for a conditional model.
I have one last question. I'd like to construct an ICC residual plot (observed proportion correct for a given theta level by expected proportion correct or the ICC) for non-technical audience who may not understand the chi-square margins. How would you do this in Mplus? As far as I understand none of the plots produced in the output can do this, but there must be a way to extract both observed and estimated proportions by theta for each item and then plot them in Excel or similar.
I think the best you can do is compare our ICC plot values for the estimated probabilities at different Theta values from the gph file with a plot of proportion correct related to estimated factor scores that you discretize into bins.