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Appendix 1: The Logistic Procedure
The logistic procedure fits linear regression models for binary or ordinal response data
by the method of maximum likelihood. In this regression, the maximum likelihood estimates
(MLEs) of the regression parameters are computed using the iteratively reweighted least
squares (IRLS) algorithm. The output includes a table of parameter estimates and tests for
the estimates. Using the parameter estimates, the estimated logit of the probability of an
event (that is, a CBAHW remaining in active practice) at different level of the exogenous
variables can be calculated as:
logit(p) = π = π 0 + π I *X I (1)
where: π 0 = intercept parameter estimate
I = vector of slope parameter estimates
X I = vector of exogenous variables
From equation (1) above, the predicted probability of an event at the given levels of
exogenous variables can be computed as:
P = e π /(1 + e π ) (2)
Other outputs of the logistic procedure include “the –2 log likelihood” (-2 log l) which
gives the contribution of the exogenous variables and “the likelihood ratio chi-squared test
statistic” for testing the significance of the exogenous variables included in the model. Also
of importance is the “odds ratio,” a measure of association which approximates how much
more likely it is for the outcome to be among those with I = 1 (active CBAHWs) than among
those with I = 0 (in active CBAHWs) at varying levels of any exogenous variable.