How do I interpret inverse prediction results of my binomial logistic regression

[#1]

Hi - I am trying to interpret the "inverse prediction" results of my binomial logistic regression.  

Below are my results....as you can see, I selected three different probabilities to evaluate (50%, 80%, and 90%), all at a 95% confidence level.  I am trying to determine how well this model predicts expected outcomes based on my observed data.

Thanks in advance!

[#2]

Under the Help menu in JMP you will find the Documentation Library.  Try searching there for 'Inverse Prediction'. You should find a section called 'Example of Inverse Prediction Using the Inverse Prediction Option', and the last paragraph gives an example of interpreting results very similar to yours.

[#3]

Thanks ih.  I'll keep probing.  While I understand what an inverse prediction is and what it does, I am uncertain how to read the meaning of the results I am getting as they do not seem to align with my raw data (which means I am misinterpreting something).  I just ran the inverse prediction again for this JMP Discussion Group response and, to demonstrate my issue, this time I am using "above 235" (i.e. if ecoli > 235, my "above 235" column equals 1, otherwise it equals 0) which is a nominal dependent variable.... vs ....turbidity (continuous independent variable).  I then ran the inverse prediction with a 95% confidence level and a 90% probability (one tail, upper 95%).  It produced  a value for turbidity of 5.3.  That is, if turbidity is > 5.3, I am 95% confident that 90% of my ecolis will be above 235.  However, my raw data suggests that this is wildly in error as only 71% of the ecolis (106 of 149) are above 235 when turbidity is > 5.3.  I would have thought that close to 90% of the ecoli instances (~134 of 149) would have been above 235 when turbidity > 5.3.  Am I missing something?

[#4]

UPDATE:   I realized I needed to change the ordering of my values.  When I did that it seems to now make sense.  Thanks again ih!

[#5 · Accepted solution]

I am a bit confused by your question.  I don't think inverse prediction is a way to see how well your model fits the data - there is information from the model fit results for that.  If you are trying to interpret the inverse prediction, the narrow confidence intervals appear to me to say that your model provides fairly precise confidence intervals for the x variable related to those probabilities of Below 235.  Since the x variable is a log, to interpret the actual confidence interval numerically would involve transforming those log values into values (through exponentiation).  I would also be careful about the inverse predictions near the extremes of the graph - depending on your data, the probabilities you specified can easily involve unrealistic values for the x variable.  For example, when I have highly imbalanced data (a small minority class to predict), high probabilities often are associated with negative values for the x variable (which is often impossible for the data I am working with).

[#6]

Hi Dale - Thanks so much for responding.  As I responded to ih a few minutes ago, while I understand what an inverse prediction is and what it does, I am uncertain how to read the meaning of the results I am getting as they do not seem to align with my raw data (which means I am misinterpreting something).  I just ran the inverse prediction again for this JMP Discussion Group response and, to demonstrate my issue, this time I am using "above 235" (i.e. if ecoli > 235, my "above 235" column equals 1, otherwise it equals 0) which is a nominal dependent variable.... vs ....turbidity (continuous independent variable).  I then ran the inverse prediction with a 95% confidence level and a 90% probability (one tail, upper 95%).  It produced  a value for turbidity of 5.3.  That is, if turbidity is > 5.3, I am 95% confident that 90% of my ecolis will be above 235.  However, my raw data suggests that this is wildly in error as only 71% of the ecolis (106 of 149) are above 235 when turbidity is > 5.3.  I would have thought that close to 90% of the ecoli instances (~134 of 149) would have been above 235 when turbidity > 5.3.  Am I missing something?

[#7]

UPDATE:  I realized I had not changed the order of my values.  When I did it seems to make sense.  Thanks again!