Path analysis with nominal outcomes
Message/Author
 Jim Shaw posted on Wednesday, September 23, 2009 - 4:39 pm
I have a student who is interested in conducting a path analysis:

(1) Y1 = X
(2) Y2 = Y1 + X
(3) Y3 = Y1 + Y2 + X,

where Y1 and Y3 are nominal (polytomous) outcomes, Y2 is a dichotomous outcome, and X is a set of continuous exogenous variables. We are receiving error messages that suggest nominal outcome variables (e.g., Y1) cannot be treated as regressors when modeling other outcome variables (e.g., Y2 or Y3). Is there any way to get around this in M-Plus, or is our only option to collapse the nominal outcome (Y1) to 2 categories and treat it as categorical in the path analysis? Also, is there any way to calculate indirect effects when modeling nominal outcomes in a path analysis? If outcomes are categorical, then I believe one may calculate indirect effects by simply multiplying the appropriate probit coefficients.
 Linda K. Muthen posted on Wednesday, September 23, 2009 - 6:10 pm
I assume y1 and y3 are unordered polytomous variables. If they are ordered, you should using the CATEGORICAL option.

Unordered polytomous variables cannot be used as mediators. As predictors, they would be treated as continuous variables which would be incorrect as they have no order.
 Jim Shaw posted on Thursday, September 24, 2009 - 5:15 am
Linda,

Thanks for the information. That is what I suspected. So it seems our only real option is to collapse the problematic variable (Y1 in this case) to two categories and treat it as categorical in the analysis. This would be analogous to collapsing health insurance from four cats (public insurance, private insurance, both, or neither) to two cats (insured or uninsured).

Is there any way to calculate indirect effects when one of the outcomes is nominal? I believe Mplus uses numerical integration when fitting models to nominal outcomes and that this precludes use of the "model indirect" statement. Using the above example, and assuming Y1 was collapsed and treated as categorical, is there any way we could estimate the indirect effect of Y1 on Y3 via Y2? For instance, could we estimate (3) with and without adjustment for Y2 and then take the difference between the adjusted and unadjusted estimates for Y1 as estimates of the variable's indirect effects? There would be a separate indirect effect estimate for each (save one) category of Y3 since Y3 would be treated as nominal in the estimation.
 Bengt O. Muthen posted on Thursday, September 24, 2009 - 9:25 am
I don't think mediation via a nominal mediator m has been studied methodologically - but correct me if I am wrong. One possible direction to go would be to create a latent class variable c where the nominal categories of c are the same as the observed nominal variable categories of m (this is done via logit thresholds). c on x is then a multinomial logistic regression and the influnce of c on y is captured by the means of y changing over the c categories (you don't say "y on c", but it has the same effect). This avoids the y on m regression which would treat m as continuous which would not make sense when m is nominal.

One can then explore if there is a need for direct effects y on x. But there isn't any guidance for how one should/could simply quantify how much of the x influence goes via m versus directly. Perhaps that isn't needed. This topic is a method research paper in itself - anyone?
 Mario Mueller posted on Friday, November 05, 2010 - 7:56 am
Hello,

is there a way to specify additional indirect effects in a SEM with a multinomial outcome, 5 binary coded and 2 continous predictor variables? The binary variables are considered to be mediated by the continous variables.

Thanks
 Bengt O. Muthen posted on Saturday, November 06, 2010 - 6:13 am
You can define indirect effects (products of slopes) using New in Model Constraint. So one for each multinomial category except the last.
 Mario Mueller posted on Wednesday, November 10, 2010 - 1:35 am
Thanks for your response. Isn't it easier to multiply the slopes and then sum up to total effects? When calculating by hand how can I obtain the p-values for the products and sums?
 Linda K. Muthen posted on Wednesday, November 10, 2010 - 11:02 am
If you calculate by hand, you then have to calculate the standard errors by hand using the Delta method to obtain p-values. I would use MODEL CONSTRAINT where you will get the standard errors and p-values automatically.
 Mario Mueller posted on Thursday, November 11, 2010 - 1:53 am
Dear Linda,

I'd rather use the MODEL CONSTRAINT option to obtain it automatically but failed. Would you be so kind to give me an example for the indirect path x1-m1-y(category1)?

My model:

analysis:
estimator=ml;
algorithm=integration;
integration=montecarlo;
MODEL: y on x1 x2 x3 x4 x5 m1 m2;
m1 on x1 x2 x3 x4 x5 ;
m2 on x1 x2 x3 x4 x5 ;

thanks,
m.
 Linda K. Muthen posted on Thursday, November 11, 2010 - 5:42 am
MODEL:
y ON m1 (p1);
m1 ON x1 (p2);
MODEL CONSTRAINT:
NEW (ind);
ind = p1*p2;
 Mario Mueller posted on Friday, November 12, 2010 - 6:56 am
Thanks Linda, it works!
Is it possible to extent that output by standardized coefficients?
 Linda K. Muthen posted on Friday, November 12, 2010 - 4:17 pm
You would need to also define those in MODEL CONSTRAINT. Example 5.20 shows this.
 Sarah Cattan posted on Friday, October 21, 2011 - 3:15 pm
Dear Linda,

I would like to estimate the following model:
Y1 on X1 X2;
Y2 on Y1 X1 X2;
where Y1 is continuous and Y2 is a nominal variable. I am using TYPE=MIXTURE to have multiple groupings.
I don't care about Mplus calculating indirect effects so I don't include the function MODEL INDIRECT.

When I try to estimate this model, Mplus tells me that it can only estimate this model with Monte Carlo integration. Could you please explain me why I can't estimate it with gaussian quadrature? I would prefer avoiding Montecarlo integration.

Thank you very much for your help.

Sarah
 Sarah Cattan posted on Friday, October 21, 2011 - 3:51 pm
Dear Linda,

Following up on my previous message, I was wondering whether I could go around this requirement of using Monte Carlo integration by renaming variables Y1 to say Y3 when it is on the right hand side. My model would thus look like the following:
Y1 on X1 X2;
Y2 on Y3 X1 X2;

This way, Mplus wouldn't notice that there is a mediating variable and would not impose the requirement of using Monte Carlo integration. Given that I am not interested in Mplus calculating the indirect effect, would this work too? By this, would the coefficient on Y3 be unbiased?

Thank you so much for your help,
Sarah
 Bengt O. Muthen posted on Friday, October 21, 2011 - 4:22 pm
The reason for Monte Carlo integration is probably because your mediator has missing data, so for some subjects it is a latent variable which together with a nominal/categorical outcome gives numerical integration. Because for some subjects it is missing and for others it is not, thereby varying the dimensionality of the integration, Monte Carlo integration is used. If you use listwise deletion you avoid this.

I don't understand why you use Type=Mixture when you specify Y2 as nominal.

I don't know how it would work having 2 copies of the mediator in the model.
 db40 posted on Friday, December 20, 2013 - 1:32 pm
Dear Dr.muthen,

I am experiencing a little confusion on how to deal with model constraints. The error I am experiencing is fatal error (ALGORITHM = INTEGRATION).

I am reading that I need to use model constraints. Would you be so kind to give me an example of how this pertains to my syntax please?

VARIABLE: NAMES ARE
....

USEVARIABLES ARE
age gender soc_sup Loneliness daily_func interpersonal
PSQ1b PSQ2a PSQ3b PSQ4a PSQ5 PSQ5a ;

categorical are
Q1b Q2a Q3b Q4a Q5 Q5a ;

missing are all (-99) ;
Weight is wt_ints1 ;

ANALYSIS:
type = general ;
ESTIMATOR= MLR ;
INTEGRATION = MONTECARLO ;
ALGORITHM = INTEGRATION ;

MODEL:
! Model A
soc_sup Loneliness daily_func interpersonal on
age gender ;

! Model B
Q1b Q2a Q3b Q4a Q5 Q5a on soc_sup Loneliness daily_func interpersonal;

! indirect effects
Model indirect:

Q1b ind age gender ;
Q2a ind age gender ;
Q3b ind age gender ;
Q4a ind age gender ;
Q5 ind age gender ;
Q5a ind age gender ;

OUTPUT:
TECH1 TECH4 ;
sampstat;
STANDARDIZED;
!mod;
 Linda K. Muthen posted on Friday, December 20, 2013 - 3:06 pm
 db40 posted on Thursday, January 30, 2014 - 6:39 am
Dear Dr.Muthen

I have used the Model constraint to estimate the indirect effects because I have binary outcome variables.

Are the parameters interpreted as linear coefficients or logistic estimates?

I used MLR if that helps.
 db40 posted on Thursday, January 30, 2014 - 7:02 am
Sorry Dr.Muthen,

I meant to add, that I have a mix of continuous and categorical variables. My mediator is continuous while my five output variables are categorical.

VARIABLE: NAMES ARE
pserial wt_ints1 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11
x12 m1 y1 y2 y3 y4 y5 ;

USEVARIABLES ARE
x1-x12 m1 y1-y5 ;

categorical are
y1-y5 ;

missing are all (-99) ;
Weight is wt_ints1 ;

ANALYSIS:
type = general ;
ESTIMATOR= MLR ;
INTEGRATION = MONTECARLO ;
ALGORITHM = INTEGRATION ;

MODEL:

y1 on m1 (p1) ;
y1 on x1-x12 (p2-p13) ;

y2 on m1 (p14) ;
y2 on x1-x12 (p15-p26) ;

y3 on m1 (p27) ;
y3 on x1-x12 (p28-p39) ;

y4 on m1(p40) ;
y4 on x1-x12 (p41-p52) ;

y5 on m1 (p53) ;
y5 on x1-x12 (p54-p65) ;

m1 on x1-x12 (p66-p77) ;

etc...
 Linda K. Muthen posted on Thursday, January 30, 2014 - 7:31 am