Marcel Grieger Mplus will pool descriptive statistics (for observed variables) and model parameter estimates across imputed data sets automatically when you fit a statistical model using TYPE = IMPUTATION or DATA IMPUTATION. So there is probably no need for you to import the imputed data sets into SPSS.

Factor means and standard deviations/variances are arbitrary (not uniquely defined before introducing arbitrary scaling/identification constraints--e.g., picking a reference indicator or fixing the factor variance and/or mean directly) in most factor models (exception: strict tau-equivalence) so the question is why you would need them / for which purpose. Factor variance estimates are output by default in Mplus, so you could simply take the square root to obtain the SD.

Because of their largely arbitrary nature, factor means are typically not relevant in (cross-sectional) CFA unless you are comparing multiple groups (multigroup CFA/SEM) or analyze longitudinal data (comparisons of means across time). Therefore, the Mplus default for single-group CFA is that factor means are fixed at zero (exception: latent growth curve models).

Hi Christian Geiser

I appreciate your insightful comment. There is little doubt that Ms/SDs have limited use in cross-sectional studies and I do my best to leave trodden paths (e. g. switching from Alpha to Omega, using MI instead of listwise or pairwise deletion, doing proper (!) EFAs - proud of that one, I might add), but in this particular case I would very much like to obtain Ms/SDs for latent variables because it is a well-established practice our discipline (Civic Education Didactics).

Bearing the limitations in mind, may I trouble you for another comment: Is there any way to "force" Mplus to give me those values under the circumstances I have laid out?

Best

Marcel

Marcel Grieger It is wonderful to see that you are adopting a lot of "modern", state-of-the art statistical techniques in your research!

You can identify latent means with ordinal items (as you could with continuous indicators). That being said, I'm "warning" you again that these means are usually arbitrary because they depend on the choice of an anchor/marker indicator or other largely arbitrary constraints. [This is why we typically estimate latent means only in longitudinal, multigroup, and/or multirater CFA. Only the differences in means (across time, groups, or raters) are meaningful (under certain assumptions/conditions such as measurement equivalence across time/groups/raters)--not the "absolute" means].

You can find an Mplus example on how to identify latent means in a single group model here:

http://www.statmodel.com/examples/webnote.shtml#web4

Download the zip folder under the link "set of examples" and take a look at the last input file (catstudye.inp). It is a multiple indicator growth model, but the principle of identifying the latent mean(s) is the same as in cross-sectional CFA. Note that one item per factor is used as anchor/marker (the item for which the loading is fixed @1 and one threshold is fixed @0) to identify the latent mean structure.

Hi Christian Geiser

thank you for your kind words and advice. Because of the help of people like yourself, I have been somewhat successful at adopting more modern techniques over the years. Also, your warning against absolute factors means is duly noted.

I followed your instructions to the letter (I hope), but I cannot detect the latent mean anywhere in the output. The only entry was under TECH 4: ESTIMATED MEANS FOR THE LATENT VARIABLES: SCK_GE = 0.0000

However, the latent mean has to be between 1 and 4 since those where the response categories on the manifest indicators.

Please find an abridged input below. Would you happen to know whether I misspecified something? I know that working through syntax is tedious ...

Cheers!

Marcel

--------

Usevar = f19_a f19_b 19_c f19_d f19_e;

Categorical = f19_a f19_b f19_c f19_d f19_e;

ANALYSIS:

type = meanstructure;

parameterization = theta;

MODEL:

SCK_Ge BY

f19_a

f19_b@1 !anchor/marker

f19_c

f19_d

f19_e;

[f19_e$1@0]; !identify the latent mean structure

OUTPUT:

Sampstat STDYX RESIDUAL Tech4;

The marker variable for which you fix the loading and one threshold has to be the same variable. Also, you need to specifically request estimation of the latent mean because it is fixed to zero by default:

[SCK_Ge*];

When you mentioned the arbitrariness of "actual" factor means, your were not kidding, were you? My factor's mean is all over the place depending on which factor loading I set to one and which of the three thresholds (Likert-scale 1-4) I fix to zero. Is this a common occurrence? If it is, there is really no point in continuing.

Since I will be asked to defend not reporting "actual" latent factor means in cross-sectional studies, I have compiled a few arguments. Do you find my string of logic sound?

- By default, latent means in Mplus are set to zero unless one compares groups or time points. The only way to get latent means in cross-sectional studies is by fixing one factor loading to one and one of the item's thresholds to zero. However, by doing so the outcome will largely be affected by the chosen loading and threshold, thus rendering the mean uninterpretable.

- Only the differences in means (across time, groups, or raters) are meaningful, not their absolute values (taken from your statement above).

- Using factor score means as a substitute (e. g. in SPSS) is not a good idea either because "factor scores are generally not good approximations of true factor values". https://www.statmodel.com/discussion/messages/9/5825.html?1459292652

--> I take this at face value, but would like to understand why this is the case. I assume it has something to do with the individual items' loading (i. e. importance for the factor) not being taken into account in factor scores.

I appreciate your patience with a layman such as myself.

Best

Marcel