Relationship to McNemar's test
In the case of one dichotomous predictor the conditional logistic regression is equivalent to McNemar's test. For example suppose we have a number of case-control pairs measuring the presence or absence of a disorder and we wish to see if they differ on rates of disprder then both approaches use the number of mismatched pairs.
Disorder Mismatch |
agegroup |
count |
Present,Absent |
1 |
5 |
Absent,Present |
1 |
3 |
Present,Absent |
2 |
4 |
Absent,Present |
2 |
5 |
Ignoring age and fitting the conditional logistic rgeression model we have a regression coefficient equal to log(9/8) which is the log of the ratio of the overall frequencies of the two types of mismatches split by age group.
The age by disorder interaction has a chi-square(1)=0.56 which is identical to that of the likelihood ratio chi-square from a 2x2 table of the four age by disorder mismatch frequencies above obtained, for example, using the CROSSTABS procedure in SPSS. If one or more mismatches do not occur it may not be possible to estimate the conditional logistic regression model coefficients (because they are not finite).