

Threshold and probability 

Message/Author 

John Lee posted on Monday, June 22, 2009  12:50 am



Hi, At the Mplus Users Guide V5 (p. 407), it was stated that the P(u=1x)=1/(1+exp(ab*x)). I have just fitted a simple model on a binary variable (0: 100 times vs 1: 200 times): TITLE: binary variable DATA: FILE IS binary1.dat; VARIABLE: NAMES x w; ! w: frequency FREQWEIGHT IS w; CATEGORICAL ARE x; USEVARIABLES ARE x; MODEL: [x$1]; OUTPUT: The followings are part of the output: SUMMARY OF ANALYSIS SUMMARY OF CATEGORICAL DATA PROPORTIONS X Category 1 0.333 Category 2 0.667 MODEL RESULTS TwoTailed Estimate S.E. Est./S.E. PValue Thresholds X$1 0.431 0.075 5.754 0.000 The estimated probability is clearly .667 (200/300). When I do the calculations based on the estimated threshold, it is P(u=1x)=1/(1+exp(0.431))=.39. Even if I use 1.39=.606, it is still different from the expected value .667. Did I miss something? Thanks. 


You should use the formula P(u=1x)=1/(1+exp(0.431))=.606 because the threshold is a. But then you also have to take into account the freqweight values. 


Also, I think you are using the formula for logistic regression rather than probit regression. 

John Lee posted on Monday, June 22, 2009  7:16 pm



Dear Bengt and Linda, Thanks for the replies. Yes, I am using the formula for logistic regression as I thought that the default link function is logistic rather than probit. In my data file, the data are: x w 0 100 1 200 where w is the frequency weight. I have also tried a version without the frequency weight. That is, I created 100 "0" and 200 "1". The estimated probability based on the formula is P(u=1x)=1/(1+exp(0.431))=.606. My concern is that the "correct" estimate on the probability should clearly be 100/300=.667. 


For maximum likelihood, the default link is logit. However, the default estimator for categorical outcomes is weighted least squares and probit regression. What you posted does not show which estimator you used. Please send your full output and license number to support@statmodel.com. 

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