How to Interpret: Generalized Regression Model with Binary (Categorical) Variables

[#1]

We’re fitting a model that tests the efficacy of a treatment (e.g., a pharmaceutical product). The DV is Recovered, a binary variable (0/1), defined as numeric nominal. The research question is whether the treatment affects the expression of a precondition and thus improves recovery. We expect that people with certain level of the precondition will react differently to the treatment, i.e., an interaction effect.

We fit a generalized regression model with binomial distribution. The predictors are 1) whether the person received treatment (Treatment; binary), 2) the variable whose expression should be affected by the treatment (Precondition, continuous), 3-4) two continuous control variables (Period and Q), as well as an 5) interaction term between Treatment and Precondition.

1. The regression equation defaults to calculate the likelihood of Recovered=0, but we’re interested in predicting Recovered=1. How do we change the default?
2. Confusingly, the parameter estimates shows the treatment parameter as “Treatment[0-1]”. Does this mean that this is the effect of no treatment or treatment? A very important distinction, obviously.
3. What’s the right way to interpret the interaction effect? Specifically, what does “-226.24” mean?

The output is below. Thanks for your help!

Generalized Regression for Recovered = 0

Model Comparison

Show	Response Distribution	Estimation Method	Validation Method	Nonzero Parameters	AICc	BIC	Generalized RSquare
[x]	Binomial	Logistic Regression	None	5	3677.7423	3708.3526	0.1934902

Model Launch

Binomial

Lasso [ ] Adaptive

AICc

[ ] Early Stopping

Logistic Regression

Model Summary

Response	Recovered
Distribution	Binomial
Estimation Method	Logistic Regression
Validation Method	None
Probability Model Link	Logit

Measure
Number of rows	6128
Sum of Frequencies	3380
-LogLikelihood	1833.8622
Number of Parameters	5
BIC	3708.3526
AICc	3677.7423
Generalized RSquare	0.1934902

Parameter Estimates for Original Predictors

Term	Estimate	Std Error	Wald ChiSquare	Prob > ChiSquare	Lower 95%	Upper 95%
Intercept	0.8755145	0.1101971	63.122825	<.0001*	0.6595322	1.0914968
Treatment[0-1]	0.0643045	0.0696953	0.8512868	0.3562	-0.072296	0.2009047
Period	0.1015936	0.0130748	60.375781	<.0001*	0.0759675	0.1272197
Q	0.0012641	0.0004935	6.5606499	0.0104*	0.0002968	0.0022314
Precondition	-0.000095	0.0001314	0.522411	0.4698	-0.000352	0.0001626
(Precondition-226.24)*Treatment[0-1]	0.0009875	0.0003172	9.6914587	0.0019*	0.0003658	0.0016093

(All the variable names are aliases due to confidentiality requirements).

[#2]

Hello, have you had the chance to review the JMP Documentation Library under the Help menu in JMP? The examples in the Documentation Library should help you to interpret your results.
Sincerely,
MG

[#3]

Thanks for the response. We did a broad search before posting the question, including in this forum, but we may have missed something. Could you point us to 1) how to change the predicted DV level and how to interpret results 2) & 3)? The numbers refer to the original questions.

[#4 · Accepted solution]

Ok, well you can change the target outcome from 0 to 1 in the Fit Model Platform Dialog. Once you have selected the Personality = Generalized Regression and Distribution = Binomial, you can select the Target Level = 1 (default is 0). In terms of interpretation you, should look at the Prediction Profiler under the Red Triangle associated with your Model Fit. The Prediction Profiler will enable you to visualize the change in Y for given changes in the X. For quantitative interpretation, in your case, you may want to save the Prediction Formula (an option under the same Red Triangle) from the model fit to column(s) in your data table. Then, you can open the formula for inspection which should assist you in your interpretation.

[#5]

Thank you! We're making progress here.

1. How do we have JMP calcualte the effect for the presence of treatment (i.e., Treatment=1). Right now, it calculates the effect of the absence of treatment (i.e., Treatment=0).
2. Just to be clear, specification of Target Level is available for Generalized Regression but not for a Generalized Linear Model, correct? At least we can't find such an option.

[#6]

1) Perhaps you can recode your data so that Treatment = 0 and rerun the model? Or, you may be able to leave it as is but change the modeling type to continuous.
2) I think you are correct. There is also the Personality = Nominal Logistic in which you can toggle the Target Level of the outcome.

[#7 · Accepted solution]

In order to have the model for Treatment = 1 instead of 0, turn on the Value Ordering property for the Treatment column. Move the 1 level up, so it is on the top of the list and re-run your model. 

You can use the same approach to predict the probability of a 1 for Recovered when using a General Linear Model.

[#8]

@G_Mand @Dan_Obermiller: Through your answers, we managed to complete the interpretation, and proceed with the research. Thank you!