# Interpreting logistic regression

I need to perform a logistic regression to to see if a group of variables which are found to be significantly associated with an outcome (by univariate tests) have significant impact on the outcome when they are put together.

In this case, from my reading, I gathered that in SPSS I need to use the enter method. When I applied this method, my new model decreased the prediction percent (not sure if this is the correct term) in the classification table in comparison to the constant only model (90.5 in constant only to 89.8 in new model). I have excluded multiple collinearity earlier.

Omnibus Tests of Model Coefficients
Chi-squaredf    Sig.
Step 1  Step    27.441  7   .000
Block  27.441  7   .000
Model  27.441  7   .000

Model Summary
Step    -2 Log likelihood   Cox & Snell R Square    Nagelkerke R Square
1               164.185a                .086                   .184

(a Estimation terminated at iteration number 6 because parameter estimates changed
by less than .001)

Hosmer and Lemeshow Test
Step     Chi-square    df     Sig.
1            6.317      7     .503


Given my objective of seeing if the independent variables when put together can have a significant impact on the outcome or not, can I use this model for that purpose to identify the variables that have and do not have independent effects on the outcome when compared together?

1. As for the "measure of predictive accuracy", could I please know it in layman's terms please? My statistical vocabulary is inefficient to answer precisely though I understand what is should mean.
2. I ran collinearity diagnostics to see there is an issue of multicollinearity between independent variables.

I cannot paste the ROC curve itself, but the tables is given below, given the values I guess I may still use the model as it is rather than changing any other parameter. Opnion on this is welcome. Thank you everyone for suggestions.

Area Under the Curve
Test Result Variable(s): Predicted probability
Area    Std. Error a   Asymptotic Sig. b    Asymptotic 95% Confidence Interval
Lower Bound             Upper Bound
.756    .042           .000              .67                           .839

The test result variable(s): Predicted probability has at least one tie between the
positive actual state group and the negative actual state group. Statistics may be biased.
a Under the nonparametric assumption
b Null hypothesis: true area = 0.5


Now I have an additional problem, or two rather 1. I have another outcome variable, again my onjective is to identify independant predictors for the given outcome amongst predictors with a p<0.01 in univariate analysis. I tried different combinations of covariates manually using the enter method, and non of a combinations seem to give a statistically acceptable models in terms of correctly classified proportions in classification tables or in ROC curves. Individially taken, these variables would give acceptable values (>0.8) in ROC despite not improving the correctly classified rates. Can I take this as being evidence of these covariants not haveing independant effects on the outcome? (number of independant variables available 7)

As the dependant variable in this is 30 day mortality, I think I can try Cox regression. However, the only time dependant variable I have is length of hospitalization, I am not too sure if I can use this at the "time" cage in SPSS.

Thank you in advance. (I am not too sure if I need to post this as a new question)

Check out the University of California Los Angeles site for detailed help on logistic regression using SPSS.

Further the link contains the annotated SPSS output with interpretations.

• Thank you very much for the suggestion, I read the given link and a number of more books and articles, however couldn't find the answer that I am looking for. That is in cases where the overall percentage in classification tables for the test model is less than that of the constant only model, how to proceed. The objective of the analysis is to check if certain indepandant variables can individually predict an outcome when thet are acting together. There independant variables were found to be significantly associated with outcomes in univariant models.. Thank you – cb80 Jul 25 '12 at 7:29

It's not unusual to see, with a relatively weak model, that the correct classfication rate (CCR) does not improve, or even drops, from what it was with a null (baseline) model. A lot of authors and analysts rely on other indicators of a model's predictive power and disregard the CCR as a general policy because it oversimplifies: it turns predictive information at the level of probability for each observation (continuous, from 0 to 1) into a binary decision (correct or incorrect classification).

However, if you find the CCR to be an important indicator in your context, you might improve results by changing your threshold for identifying a case as "1" as opposed to "0". SPSS's default is to call a case "1" if the predicted probability is over .5, but you may decide to use a threshold of, say. .4 or .35. I say this realizing that it can take on the aspect of "cherry picking" and may open you to criticism. It's best to change this threshold only if you have a theoretical basis for doing so--not merely to improve the CCR after the fact.

Another approach is to examine ROC curves, which you can obtain from SPSS in a different menu if you first save each observation's logistic regression predicted probabilities. Through the ROC procedure you can check those probabilities' matchup with the values on the binary outcome variable.

• Thank you very much, extermely helpful. I will perform ROC and see if the model is "fitting". – cb80 Jul 25 '12 at 13:44
• @cb80 You will need to register your account to post comments and access system-wide notification. In the meantime, I've merged your two accounts. – chl Jul 25 '12 at 14:04
• +1, nice points @rolando2. I can imagine someone arguing that using a different threshold is "cherry picking", but I wouldn't agree w/ them; you haven't changed what covariates are included, your alpha, etc., & other global model quality metrics would be unchanged. In general, w/ LR, unless I misremember, classification accuracy is maximized if the threshold is equal to the proportion of 1's in the population (which, in practice, is assessed by the proportion in your sample). Eg, if 35% get sick, predict that a given patient will get sick if $\hat p>.35$. – gung - Reinstate Monica Jul 25 '12 at 14:48
• Thanks gung. That sounds like an intuitive strategy but such things are often deceiving. Can you think of a reference or two on that--or can others weigh in as to whether they have found it to be true? – rolando2 Jul 26 '12 at 12:07