ML vs. WLSMV with continuous and cate...
Message/Author
 Mark Wade posted on Friday, March 02, 2012 - 8:41 am
I am running a simple SEM in which I have an observed predictor and mediator. The outcome variable is a latent factor with four indicators, one of which is categorical (the others are continuous).

I understand that the ML and MLR estimator can be used for both categorical and continuous variables, whereas the WLSMV is appropriate for categorical outcomes. However, when there are both kinds of indicators, it is my understanding that numerical integration is required. Such a procedure precludes use of the 'model indirect' command in Mplus.

By not specifying the categorical variable with the CATEGORICAL ARE function, direct and indirect estimates can be attained with the use of ML or MLR estimation. Is there some other way to attain the indirect effects when the latent construct consists of both continuous and categorical indicators? Is it inappropriate to not specify the categorical variables when performing ML or MLR?

Thank you.
 Linda K. Muthen posted on Friday, March 02, 2012 - 11:43 am
WLSMV can be used with a combination of categorical and continuous indicators. It can't be used with only continuous indicators. So it sounds like you can use WLSMV and MODEL INDIRECT.
 Aylin posted on Tuesday, May 22, 2012 - 10:26 am
Dear Linda,

I am running a structural equation model using the WLSMV estimator. I am a bit puzzled with 2 things 1)the probit and linear regressions; 2) choosing the standardized results. I want to make sure I understand it correct:

Factor as covariate -> outcome as factor = Linear Regression (STD)
Factor as covariate -> outcome as observed categorical = Probit regression (STDY)
Factor as covariate -> outcome as observed continuous = Linear regression (STDYX)
Observed categorical as covariate -> outcome as factor = Linear Regression (STD)
Observed continuous as covariate -> outcome as factor = Linear Regression (STD)
Observed categorical as covariate -> outcome as categorical = Probit regression (STDY)
Observed continuous as covariate -> outcome as categorical = Probit regression (STDY)
Observed categorical as covariate -> outcome as continuous = Linear Regression (STDYx)
Observed continuous as covariate -> outcome as continuous = Linear Regression (STDYx)

Are these correct??
 Linda K. Muthen posted on Tuesday, May 22, 2012 - 11:04 am
If your dependent variable is continuous, you obtain a linear regression. If your dependent variable is categorical, you obtain a probit regression.

When covariates are observed continuous, you use StdYX. When covariates are observed binary, use StdY.

When either a dependent variable or a covariate is latent, use STD.
 Aylin posted on Tuesday, May 22, 2012 - 2:27 pm
Thanks a lot Linda.
But what if my output does not shot STDy.Even though I have binary variables and look at the relationships between them. Does that mean there is something wrong with the model?
 Linda K. Muthen posted on Tuesday, May 22, 2012 - 2:39 pm
No, nothing is wrong with the model. You need to create it yourself if it is not given. See the STANDARDIZED option for standardized formulas.
 Aylin posted on Wednesday, May 23, 2012 - 2:23 am
Dear Linda,

I checked the manual and found out it must be

bstdyx = b*SD(X)/SD(y)

my only problem is where will i see the standard deviation? As I have imputed some cases in my mplus, I can not just check it from my SPSS descriptive.

Or did I understand it wrong?
 Linda K. Muthen posted on Wednesday, May 23, 2012 - 12:24 pm
You should use the values from TYPE=BASIC.
 Edwin Wouters posted on Friday, May 31, 2013 - 7:39 am
Dear Linda,
I am running a structural equation model:
NAMES ARE
Education NumberRooms Income Hunger
Emotional Tangible Affectionate Positive
Stress Depression Smoking;

CATEGORICAL ARE
Depression Smoking;

USEVARIABLES ARE
Education NumberRooms Income Hunger
Emotional Tangible Affectionate Positive
Stress Depression Smoking;

ANALYSIS:
Estimator = WLSMV;

MODEL:
SES by Education NumberRooms Income Hunger;
SocSupp by Emotional Tangible Affectionate Positive;

SocSupp on SES;
Stress on SES SocSupp;
Depression on Stress SocSupp;
Smoking on SES SocSupp Depression;

OUTPUT: STDYX TECH4;

Now you see that I have a mixture of endogenous categorical (binary) and continuous outcomes. If I run this model I get unstandardized and STDYX coefficients, each time with SE and significance level.

My questions:
1) How should I interpret this long list of coeffients? Is it correct that the numbers after "SocSupp by SES" (two latent variables) are linear regression coefficients and that the numbers after "Smoking on SES SocSupp Depression" (categorical dependent) are Probit coefficients? And they are mixed in the output list?
2) Above (post by Aylin) I see that sometimes you need to use UNSTD, STD, STDY, STDYX coefficients. In my example: when should I use which?

Many thanks in advance,
Edwin
 Bengt O. Muthen posted on Friday, May 31, 2013 - 8:25 am
1) Yes.

2) See the UG on advice for choice of standardized - check the Index for STANDARDIZED.
 Edwin Wouters posted on Monday, June 17, 2013 - 6:43 am
Thank you very much for this information, Prof. Muthen.

I have consulted the UG on standardization, but I am not fully sure whether I get everything. Let me say what I think it is:

SES (latent) -> Stress (continuous): use STD
Social Support (latent) -> tress (continuous): use STD
SES (latent) -> Social Support (latent): use STD
Stress (continuous) -> Depression (binary): use STDYX
Social support (latent) -> Depression (binary): use STD
SES (latent) -> Smoking (binary): use STD
Social Support (latent) -> Smoking (binary): use STD
Depression (binary) -> Smoking (binary): use STDYX.

Is this correct? If yes, then I think I get it...

Many thanks,
Edwin
 Linda K. Muthen posted on Monday, June 17, 2013 - 12:58 pm
For models without covariates use StdYX. For structural parameters, StdYX is the same as Std.

For models with covariates, use StdYX if the covariate is continuous, use StdY if the ovariate is binary.
 Dick Durver posted on Tuesday, July 30, 2013 - 4:36 am
Dear Linda,
I have read all this information (and also consulted the UG) but I am still not sure that I get it completely. To not create extra work, I will work with the example above (by the previous member) and I try to correct his strandardizations:

SES (latent) -> Stress (continuous): use STD
Social Support (latent) -> Stress (continuous): use STD
SES (latent) -> Social Support (latent): use STD
Stress (continuous) -> Depression (binary): use STDYX
Social support (latent) -> Depression (binary): use STD
SES (latent) -> Smoking (binary): use STD
Social Support (latent) -> Smoking (binary): use STD
Depression (binary) -> Smoking (binary): use STDY.

I think this is correct, right?

So, for all structural paths, you only look at the independent variable:
1. If this is binary, you use STDY
2. If this is continuous, use STDYX
3. If this is latent, use STD...

Many thanks, because I am currently performing such a structural analysis (including latent, binary and continuous (in)dependent variables for somebidy else. So it needs to be correct...

Dick
 Bengt O. Muthen posted on Tuesday, July 30, 2013 - 6:09 am
A simple rule is:

If the IV is continuous (latent or otherwise) use STDYX and if it is binary use STDY.

This simple rule works also with latent variables where no observed X or no observed Y is involved because the standardization with respect to the latent variable is included when doing STDYX and STDY. For instance, if both the IV and DV are latent, STDYX=STD.

So, you could say:

1.SES (latent) -> Stress (continuous): use STDY

2.Social Support (latent) -> Stress (continuous): use STDY

3.SES (latent) -> Social Support (latent): use STDY

4.Stress (continuous) -> Depression (binary): use STDYX

5.Social support (latent) -> Depression (binary): use STDY

6.SES (latent) -> Smoking (binary): use STDY

7.Social Support (latent) -> Smoking (binary): use STDY

8.Depression (binary) -> Smoking (binary): use STDY.

Note that 3. gets the same results as STD.
 Dick Durver posted on Tuesday, July 30, 2013 - 8:44 am
Thanks! I will try to apply this knowledge to my own models. :-)
 Anke Schmitz posted on Tuesday, July 15, 2014 - 7:16 am
Dear Drs. Muthen,
when estimating interactions between latent variables and observed variable with WLSMV the output reports unstandardized coefficients only. Is that right or do I have to report standardized coefficients?
Anke
 Bengt O. Muthen posted on Wednesday, July 16, 2014 - 11:52 am
I think I answered this in an earlier post, where XWITH was the cause of not giving standardized.
 Edwin Wouters posted on Wednesday, September 21, 2016 - 12:54 am
Dear Prof Muthen,

Just wondering which standardisation I should report when analysing:

binary --> latent (STDY?)
continuous --> latent (STDY?)

Thanks so much
 Bengt O. Muthen posted on Wednesday, September 21, 2016 - 5:14 pm
See the UG under Standardized.
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