-------------------------------------------------------------------------
Help for ulogit: Univariate log-likelihood tests for model identification 
-------------------------------------------------------------------------

The syntax for ^ulogit^ is:

                    ^ulogit^ depvar predictors
     

Comparing the log-likelihood of a logistic regression model containing only 
the intercept with that of a model having a single predictor provides prima 
facie evidence of whether the predictor in fact contributes to the model. 
The comparison statistic is provided by the likelihood ratio test. At the 
early model building stage, a p value of .25 or under can be considered 
adequate for inclusion of the variable as a main effect predictor. However, 
this does not mean that transformation or collapsing value levels may not 
prove to later enhance a variables contribution to a full model. What we 
are really looking for at this stage are high p values. If we find one at 
say .80, we can probably exclude it from subsequent analyses. But a caveat 
- if the variable may serve as a factor in a significant interaction, we 
may need to retain it regardless of its p value.

^ulogit^ calculates for each variable listed after the response variable, 
its coefficient, log-likelihood, Chi-square (LL ratio statistic), 95% 
confidence interval, and significance. The intercept only model log-likelihood 
is also provided for comparison. Predictors must all by numeric.

The intercept only log-likelihood can be calculated directly from the 
distribution of the reponse variable. Let n0 and n1 represent the respective 
number of observations having 0's or 1's; and let N be the total number of 
nonmissing observations. The log-likelihood can be determined by:

               ^LL = n0 ln(n0) + n1 ln(n1) - N ln(N)^
            
After the ^logit^ command, one can also obtain the LL statistic directly 
from Stata by:

               ^LLo = -(_result(6)+(-2*_result(2)))/2^
            
where _result(6) is the chi2 and _result(2) is the log-likelihood of the 
model with predictor(s).


The likelihood ratio test evaluates the hypothesis that the slope coefficient
is zero. Given LL1 as the log-likelihood of the model with the predictor, 
and LL0 as the intercept only log-likelihood, the ratio is determined by:

                        ^chi2 = 2(LL1 - LL0)^


Reference:
Hosmer, D. W. and Lemeshow, S.  1989.  Applied Logistic Regression. 
New York: John Wiley & Sons.


See Also: ^unilogit^ by author in STB-9 (sqv5) for alternative table



Author and help:

^Joseph Hilbe^
Arizona State University
^hilbe@@asu.edu^
jhilbe@@aol.com

