Title: Building a model - SPSS outputs
Course: UGQuants (SSPS) > Section: Logistic Regression

Building a model - SPSS outputs

The classification table shows how the regression model has predicted the values of the dependent variable based on the values of the various independent variables and compares these with the values each case actually took: the observed values.  Since in this first stage of the model there are no predictor variables, the regression simply chooses which observed value is most common (the mode) and predicts all cases to take this value.  It gets all these cases 'correct' for cases that do take the modal value, and wrong for all others (underlined in red).

Ignore the second output box, as we are not really interested in the 'performance' of this model as such, but only in how much we can improve it.

The third box 'Variables not in the equation' calculates the significance value for the variable that has not yet been entered (agea), or the probability that the real value of the odds ratio corresponding to its logit is one and that it thus makes no difference to our ability to predict the value of our dependent variable.  The probability of this is zero to three decimal places, so that we can be pretty sure that age does make an improvement to our model, although we do not yet know by how much ...

The next step thus enters agea as a continuous independent variable, and we obtain the output shown below:

The first two tables show the performance of our new model as a whole.  The 'log likelihood' is the natural log of the probability that the observed values of the dependent variable can be predicted from the model.  Because it is a log of a number between zero and one (zero would be a totally useless model and one would be a perfect one) it is negative.  Multiplied by -2 it becomes a positive number.  The size in itself is much less important than its size relative to the size of the -2LL figure for  other model specifications, such as the first model with no independent variables.  This gives us the LL ratio.  This figure is used to calculate the model Chi Sq and its associated significance.  In this case our model is statistically significant; that is to say, at least one of the predictors must have an effect.  Since we have only one, it must be age!

The two versions of R squared in the model summary table are basically measures analogous to R squared in linear regression.  Generally speaking Nagelkerke's R squared is to be preferred to the Cox & Snell version, as it produces a range of values more similar to that of R squared in OLS linear regression.

As an aside: do NOT confuse the model Chi Sq significance with another useful measure that you can ask SPSS to provide, the Hosmer and Lemeshow goodness of fit test.  This tests the difference between the distribution of the observed and predicted results, so that if our model is a good one, the result should be non-significant.

The Variables in the Equation box give us the key results for the individual independent variables in our model.

B is the logit of the independent variable.  It tells us the natural log of the change in odds of the dependent variable taking the value 1 associated with a unit change in the independent variable.  It is profoundly non-intuitive, so we can afford to ignore it most of the time.

Next to this is the standard error of this logit and the associated Wald statistic.  While it is still widely used, we should be careful of the Wald statistic as it is now regarded as giving unreliable results in certain circumstances (when the coefficients are large or dummy variables are used).

We should concentrate our attention on Exp (B).  This converts the logit of -.029 into the odds ratio for a one unit increase in age.  It does so by taking the exponent of the log (thus converting the log back into an ordinary number: the odds).  It is just below one and tells us that for each additional year of age of our respondents, the odds of disagreeing with the statement decreases by 2.9% (1 – 0.971*100)

Thus we have confirmed that age does appear to be a substantial predictor of attitudes to the idea that men have more rights to a job than women.  You can also ask SPSS to calculate a 95% confidence interval for this statistic.  If this interval includes the value 1 (which equates to no change in the odds) then we do not have sufficient evidence that our independent variable is useful in predicting the distribution of cases across our dependent variable

The classification table shows how well our new model predicts values for our dependent variable.  We have correctly predicted 96.5% of those who disagree with the statement and 13.9% of those who do not, giving a correct classification for over 70% of cases.  Strictly speaking, we should consider this in relation to the initial (null) model, to see how much improvement there is in the classification.  In this case, the improvement is equivalent to 70.3 – 68.2 = 2.1%.

What next? Controlling for age, does religion still have an impact?