Multinomial IV in monte carlo simulation PreviousNext
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 Joseph E. Glass posted on Monday, March 07, 2011 - 4:34 pm
For the purpose of power analysis, I am attempting to use monte carlo simulation to generate a four category observed nominal variable. I will regress a continuous(observed) independent variable on this nominal variable. I am having trouble locating examples that show how to generate a multinomial independent variable for such a monte carlo simulation. Any suggestions on how to approach this?

Thank you.
 Bengt O. Muthen posted on Tuesday, March 08, 2011 - 12:15 am
So you want to regress y on c, where y is continuous observed and c is nominal observed.

You can do this in Mplus by working with a latent class variable that is identical to your nominal variable. How to do this is shown in a FAQ on our web site. The influence of c on y is portrayed by the y means changing as a function of the classes. You don't say "y ON c".
 Joseph E. Glass posted on Tuesday, March 08, 2011 - 1:40 pm
Thank you for your guidance on this. I am not sure what this would involve so it is difficult to know what FAQ or documentation to look for on the web site. Could you point me to these materials?
 Bengt O. Muthen posted on Tuesday, March 08, 2011 - 2:12 pm
It is called:

"Making an observed nominal variable u equivalent to a latent class variable c"
 Joseph E. Glass posted on Monday, March 14, 2011 - 4:59 pm
I have two follow up questions. Q1: Regarding the document that you referred me to, "Making an observed nominal variable u equivalent to a latent class variable c", I suppose that you are able to manipulate the threshold values that you specified to change the proportion of individuals that fall into each class. Would you give guidance or refer me to a reference that describes how to specify thresholds to create the nominal variable appropriately?
Q2: What model setup would I use to portray the y means varying as a function of the classes? I hope to use monte carlo simulation to determine the power to detect significant differences in y across classes.
Thank you.
 Linda K. Muthen posted on Tuesday, March 15, 2011 - 3:52 pm
1. You need to give the program the intercept values in a logit scale. Let's say you want the proportions of a three-category nominal variable to be .20, .30, and .50 where .50 is the reference class. You need to give logit values for the first two classes. You compute them as the log of the ratio of the probability of being in one class to the probability of being in the reference class, for example,

log (.20/.50) and
log (.30/.50)

2. Add the y means to the MODEL and MODEL POPULATION commands. Example 8.6 has a distal outcome. Look at the Monte Carlo counterpart to that example.
 mpduser1 posted on Thursday, June 02, 2011 - 8:14 pm
I am trying to perform a Monte Carlo power analysis for a multinomial logistic regression model in Mplus. I wish to have my dependent variable (Y) be a 3-level nominal categorical variable, while my predictor (X) is dichotomous. I've been experimenting with the Mplus syntax and have found something like the following to work:

NAMES ARE Y X;
NOBSERVATIONS = 500;
GENERATE = Y (n 3);
NOMINAL = Y;
CUTPOINTS = X(0);


MODEL POPULATION:
X*.50 ;
[X*.50] ;
Y#1 on X*.3;
Y#2 on X*.4;
Y#3 on X*.5;

ANALYSIS: TYPE = GENERAL;
ESTIMATOR = ML;

MODEL:
Y#1 on X;
Y#2 on X;
Y#3 on X;

My question is why does Mplus require me to specify a regression model for Y#3 -- isn't Y=3 the baseline for my multinomial logistic regression model?
 Bengt O. Muthen posted on Thursday, June 02, 2011 - 10:01 pm
Page 694 of the UG says (see u7) that y(n 3) implies a nominal variable with 4 categories and with 3 intercepts. So it is correct that you wouldn't mention the last category in your MODEL statements.
 mpduser1 posted on Thursday, June 02, 2011 - 10:49 pm
With regard to specifying means for the dependent variable in the POPULATION portion of my sintax, i.e., via:

[Y#1@-1.26];
[Y#2@1.73];
<etc.>

Is it correct that these are the intercepts of my categorical Y after adjusting for my predictor variable, X?

Thanks.
 Linda K. Muthen posted on Friday, June 03, 2011 - 4:06 pm
Thresholds for categorical variables are specified using the $ not #.

These are the intercepts in the regression of y on a set of covariates. They are given as thresholds which have the same value but opposite sign of intercepts.
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