Greetings, The new skew SEM possibilities are really great! I have some questions regarding practical implementation. (1) Typically, models use a number of variables that may fit normality assumptions to various degrees. (a) Thus, how would you recommend we pick which one of the three available distributions(skewnormal, skewt, t)? Maybe start with SKEWT and look at the indicators of skewness and df? Would a SKEWT analysis be in any way biased if the data are more SKEWNORMAL or T (I think not as even normal data seems correctly estimated with SKEWT based on your paper)? Would you recommend any specific guideline to select the distribution? (b) I also saw that you can select specific variables in a single model for which to use the SKEW distributions (but not the others). Any guideline to suggest to determine the level of skewness that justifies dropping normality assumptions for a specific variable? (2) Many studies used Likert items (ordered-categorical). Simulations showed that treating these variables as continuous and using ML/MLR estimation is robust as long as there are more than 5 answer categories, whereas WLSMV tends to be better with less categories. You mention that the SKEW estimators are designed for continuous data. How does that translate to Likert items? For instance, would there be any problems in using MLR with a SKEW distribution with Likert items with 6-7 answers categories?
I'd try a sequence: Normal, t, skew-normal, skew-t. If the skew and kurtosis is small (say less than plus minus 0.5?) you might get a better BIC with normal. But using say a skew-t would not hurt but simply get skew approx = 0 for more normal variables. Skew-normal can't accommodate skews larger than plus minus 1. We've had problems fitting skew-t with Likert scales, at least if all answer categories don't have high frequency, but more experience is needed.
Courses dealing with these new features are listed on our website. There will be handouts from these courses posted on our website shortly. There is a handout posted already from my 5/6/14 presentation to PSMG. There will be a videotaping of the July Psychometric Society 1-day training on this that we will post.
I have tried factor mixture analysis with non-normal distributions using the newly released version 7.2 and have a few questions regarding this new analysis:
1) In your mixture examples in Webnote 19, MLF and ML were used as estimators instead of the default MLR. Which estimator(s) do you deem suitable for non-normal mixture modeling? Tech11 is not available without using MLR. Do you think it is essential to use MLR to obtain Tech11 or it is okay to simply rely on BIC for model comparison?
2) The 2-class, 2-factor FMA with t gives a much smaller BIC over the FMA with normal and its results make substantial sense. The model warns about the low df parameters (2.77 and 2.91) and infinite skewness in both classes. May I ask what are the distributional assumptions of the skew-t distribution and how should one interpret the infinite skewness?
3) In page 10 of Webnote 19, it is written that ‘models with v < 3 should be used only for modeling data with substantial heavy tails and outsiders’, does this mean that I should not go on to perform FMA with skew-normal or skew-t as their results would not be valid in my case of infinite skewness and should instead focus on the FMA results with normal and t?
1) I would use MLR. At first we had only MLF available so that's why that was used in some early runs posted. I would simply use BIC.
2) Come to our UConn Mplus Version 7.2 course on Monday and we'll talk about it. It's a long story. Briefly, you can still describe (and plot) the estimated distribution so in that sense it is ok. Small df can come from smallish class sizes - I think your total sample size as n=197 which is not a lot in this context. Also, we do need more practical experience.
3) Look at your histograms to see if you have heavy tails - that is large positive kurtosis value (see View Descriptive Stats). You can certainly try skew-normal and see how the BIC compares, but skew-t may be out of reach for this small sample.
I am trying to run an SEM growth model using the newly released 7.2 with skewed distributions. I am not able to get the models to run. The output states the following: THE MODEL ESTIMATION DID NOT TERMINATE NORMALLY DUE TO AN ERROR IN THE COMPUTATION. CHANGE YOUR MODEL AND/OR STARTING VALUES. Do you have any suggestions? I have been investigating zero inflated models for this data because it has about 30% of density at 0. Thank you.
I have the same error as Janice Kooken, who posted on Thursday May 29, 2014. I am curious if you have any suggestions for dealing with this error. I initially tried to run the measurement model for two scales with the latent factors predicting some skewed outcomes. All in one place produced errors, but even taking the observed scores and attempting to predict the skewed outcomes one by one produced errors. I also tried increasing the number of random starts. In addition to skew I have some floor and ceiling effects. I am wondering if it is that these data aren't appropriate for these options, or if I am not using the options correctly!
Floor and ceiling effects was the issue that Kooken had if I remember correctly. It appears that skew-SEM can have problems with that since it is an extreme case of skewness that is probably better modeled in other ways such as two-part modeling with parameters describing the probability of being at the floor or ceiling. If you like you can send the data and input to Support so we can all learn more about this.
Dr. Muthen, Thanks for your reply. You are correct about Kooken, I spoke with her directly! We have considered the zero-inflated Poisson model for one of our outcomes, but were interested learning more about these new skew options. I will send along the data and input, to get your thoughts!