Logistic regression using replicated ... PreviousNext
Mplus Discussion > Multilevel Data/Complex Sample >
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 gibbon lab posted on Monday, December 10, 2012 - 7:08 pm
Dear Professor,

I am running a simple logistic regression using replicated weights. Here is my code

DATA: FILE IS D:\lzg\Adsdata\alcohol\spss_alc.dat;

VARIABLE: NAMES ARE finedwt0 ... gender10;

categorical are moresip_any;

WEIGHT=finmedwt0;
REPWEIGHTS=finmedwt1-finmedwt160;

MISSING ARE ALL (9999);

Analysis:
TYPE =complex;
REPSE=JACKKNIFE1;

MODEL:
moresip_any on scalealctrim2;

OUTPUT: SAMPSTAT;
STANDARDIZED;
MODINDICES(3.84);

Part of the output:
Estimator WLSMV

MODEL RESULTS
Two-Tailed
Estimate S.E. Est./S.E. P-Value

MORESIP_ ON
SCALEALCTR 0.467 0.037 12.541 0.000

Should I calculate the Odds ratio as exp(0.467)=1.60?

I did the sample simple logistic regression using repweights in SAS, but got a very different result (OR=1.19). Is it because I did not interpret the Mplus output correctly? Thanks a lot!
 Linda K. Muthen posted on Tuesday, December 11, 2012 - 2:24 pm
If you are using WLSMV, you are not getting a logistic regression coefficient. You are getting a probit regression coefficient which cannot be exponentiated. Ask for a maximum likelihood estimator to obtain logistic regression.
 gibbon lab posted on Tuesday, December 11, 2012 - 4:23 pm
Dear Linda,

Thanks for the prompt response. I tried to specify "ESTIMATOR=MLR;" as in the following

Analysis:
TYPE =complex;
REPSE=JACKKNIFE1;
ESTIMATOR=MLR;

But the output still gave me WLSMV estimator. I also tried "ESTIMATOR=ML;", it gave me WLSMV too. Is there any other option to force the program generating MLE? Or only WLSMV is available for replicated weights?

By the way, can you give guidance on how to interpret the probit regression coefficient? Is there a way to convert it to an odds ratio?
 Linda K. Muthen posted on Tuesday, December 11, 2012 - 4:42 pm
Maximum likelihood is available with replicate weights only with continuous outcomes.

See the Topic 2 course handout and video on the website where probit regression is discussed. Probit regressions coefficients cannot be converted to an odds ratio.
 gibbon lab posted on Tuesday, December 11, 2012 - 8:03 pm
Dear Linda,

I tried to use TAYLOR method this time for estimating the variance. My code is

DATA: FILE IS D:\lzg\Adsdata\alcohol\spss_alc.dat;

VARIABLE: NAMES ARE finedwt0 ... gender10;

categorical are moresip_any;

WEIGHT=finmedwt0;
CLUSTER=tspsu;

USEVARIABLES ARE moresip_any scalealctrim2;

MISSING ARE ALL (9999);

Analysis:
TYPE =complex;
ESTIMATOR=MLR;

MODEL:
moresip_any on scalealctrim2;

This time I got an Odds Ratio (2.29). But it is still not the same as what I got in SAS (1.20) using the same model. Was something wrong with my coding? The output did not give any error message. Thanks.
 Linda K. Muthen posted on Tuesday, December 11, 2012 - 8:33 pm
Send both the Mplus output and the SAS output in a format I can read along with your license number to support@statmodel.com.
 matthew finster posted on Wednesday, December 12, 2012 - 10:31 pm
Dear Linda,

Is it possible to conduct a multi-nominal logistic regression model with complex survey data using weights and replicate weights? If so, which estimator should I use?
 Linda K. Muthen posted on Thursday, December 13, 2012 - 12:17 pm
This is not possible with replicate weights. They are available for continuous outcomes with maximum likelihood and for categorical outcomes with weighted least squares which gives probit regression.
 gibbon lab posted on Thursday, December 13, 2012 - 7:43 pm
Dear Linda,

I read the Topic 2 course handout on the website. Noticed an interesting relationship between logit and probit was given in the handout:

logit(p) approximately equals probit(p)*1.81 for any probability p.

Can this relationship be used to convert probit coefficient to odds ratio? For example, given a probit coefficient is beta, isn't the approximate OR=exp(beta*1.81)? Thanks a lot!
 Linda K. Muthen posted on Thursday, December 13, 2012 - 8:20 pm
No.
 gibbon lab posted on Thursday, December 13, 2012 - 11:21 pm
Dear Linda,

As a follow up on the interpretation of probit regression, can you give a specific reason why that relationship can not be used to calculate approximate OR?

Given the approximation between logit and probit, I feel like it can be shown that

Phi(alpha+beta*x)=expit(1.81*alpha+1.81*beta*x)....(1)

Here Phi is the N(0,1) distribution function and expit denotes the inverse of logit.

Based on equation (1), the approximation of OR=exp(1.81*beta) seems reasonable.
 Linda K. Muthen posted on Friday, December 14, 2012 - 6:34 pm
Rescaling the probit coefficient does not change its properties. It is the properties of the logistic coefficient that make it able to be exponentiated in a meaningful way. I think you would have a difficult time getting this past a reviewer. In the past, this rescaling was used to put the probit in a logit metric. To see that it is approximate, do a logistic and probit regression. Scale the probit coefficient and exponentiate the logistic and rescaled probit coefficients and see how close the values are.
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