Logistic regression with multiple outcome variables

[#1]

I am running logistic regression analyses on a dataset where the outcome has multiple categorical variables.  In this case, I am using total number of humans present (continuous variable) to predict the behavior of gibbons (the behaviors are categorical).  I am trying to use the parameter estimates to determine which specific behaviors are affected by the number of humans, but I am having trouble interoperating the results.  I can see the results for each individual behavior, and the Wald test to show whether that behavior is affected by number of people, but the last behavior alphabetically on my list (vocalize) does not output any numbers, so I do not know how to see if this variable is affected.  Am I interoperating these results correctly?  How do I see if the last behavior (vocalize) is affected by number of people?

[#2]

Yes, each row (individual) will get a result from the formula for the odds.

Yes, you can use the mean odds. Use Table > Summary or Analyze > Tabulate to get the results for each group or subgroup.

The hand calculation is as you say Pr(group A) divided by Pr(not group A) or whatever. The odds ratio would be the ratio of the odds under different conditions (treated, untreated).

[#3]

Hi Mark,

I am performing a multinomial logistic regression for an outcome variable with three levels.  I have been trying to figure out how to find the odds ratios and finally came across this previous answer from you. 

How do I save the probability formulas?

Thank you in advance.

[#4]

Click the red triangle at the top of the platform and select Save > Save Probability Formula.

[#5]

Thank you for the prompt response. 

Alternative to saving the probability formulas and calculating the odds ratios myself, I had independently saw at the bottom of the parameter estimates data display on my multinomial logistic model that is says "for log odds of Outcome A/Outcome C, Outcome B/Outcome C" where Outcome C is my reference outcome.  Is it possible that I can just calculate the odds ratio by transforming this data into a data table, inserting a new column with the formula exp(Estimate)? 

I found a separate post that references this as well -->  https://community.jmp.com/t5/Discussions/Logistic-regression-with-multiple-outcome-variables/m-p/110...

It seems almost too easy to be true.

Thank you again.

[#6]

It is not true. That way is also not easy at all. It is more difficult than using the Save command. The parameter estimates are not estimates of the odds or odds ratios. That note is just a re-statement of the logistic regression problem. You have the linear predictor on the right side of the model equation and the logit function on the left side. The note that you see at the bottom of the Parameter Estimates table is just a record of what logits were used with the linear predictors.

If you save this table of estimates, then you have to create a column formula to compute the logit value for each row. Then you have to add another column formula for each response level to back-predict the probabilities. That is what the Save > Save Probabilities command does for you.

[#7]

I am using JMP 13 Pro, not a student version. 

[#8]

Are there tutorials/videos for logistic regression with multiple outcomes?

[#9]

I checked our learning assets but found no tutorials about nominal logistic regression. (See items from selecting Learning JMP on the JMP home page menu.) I then checked our YouTube account and found this tutorial about Multiple Logistic Regression. There is also Logistic Regression Introduction with Tutorial in JMP on YouTube. It covers logistic regression more thoroughly but only for the outcome. It does not cover multi-nomial logistic regression.

We offer this training course, which covers this topic: Analyzing Discrete Responses. We cover the origin, use, and interpretation of such models as well as how to preform this regression in JMP.

[#10]

You can't do logistic regression with multiple dependent variables in one run of logistic. But perhaps you have ONE dependent variable - behavior of gibbon - with multiple levels?  How is "behavior" operationalized? Is the data something like this:

Case ID Num People      Behavior

1               3                    A

2               2                    B

3              5                     A

4              2                    C

etc.? Or does each gibbon engage in multiple behaviors? Or is each gibbon engaged in multiple cases? (in that case, you'd need some form of multi-level model, probably with GLIMMIX?

[#11]

It is like you have laid out.  The gibbon only does one behavior at a time, but it has several behaviors it can do, such as feed, travel, vocalize, groom, etc.  What I am trying to do is see how the number of people present affects the likelihood of the gibbon doing a certain behavior e.g. does the gibbon reduce time spent feeding when more people are present.  The logistic regression tells gives me a p value for the entire model, so I can see that number of people does affect gibbon behavior, but what I would like to do is see which individual behaviors are driving the model - I'd like some sort of stats with p values that show me which behaviors are actually changing.  All I am doing now is looking at the output figure and describing how the behaviors change.  Here is what the output looks like.  I tried to insert the figure, but it wasn't working.  I have figured out though, that I cannot do the odds ratio test because my response (behavior) has more than 2 variables. 

Logistic Fit of Behavior By total humans

Whole Model Test

Model	-LogLikelihood	DF	ChiSquare	Prob>ChiSq
Difference	37.2401	11	74.48025	<.0001*
Full	1162.7796
Reduced	1200.0197

RSquare (U)	0.0310
AICc	2371.15
BIC	2468.39
Observations (or Sum Wgts)	660

Measure	Training	Definition
Entropy RSquare	0.0310	1-Loglike(model)/Loglike(0)
Generalized R-Square	0.1096	(1-(L(0)/L(model))^(2/n))/(1-L(0)^(2/n))
Mean -Log p	1.7618	∑ -Log(ρ)/n
RMSE	0.7987	√ ∑(y-ρ)²/n
Mean Abs Dev	0.7918	∑ |y-ρ|/n
Misclassification Rate	0.6727	∑ (ρ≠ρMax)/n
N	660	n

Parameter Estimates

Term		Estimate	Std Error	ChiSquare	Prob>ChiSq
Intercept[Drink]	Unstable	9.3119005	1537.0201	0.00	0.9952
total humans[Drink]	Unstable	-13.895268	1537.0192	0.00	0.9928
Intercept[Feed]		-1.5746952	0.2067421	58.01	<.0001*
total humans[Feed]		0.45943506	0.0703651	42.63	<.0001*
Intercept[Groom]		-3.8964691	0.7363762	28.00	<.0001*
total humans[Groom]		0.17142825	0.2657919	0.42	0.5189
Intercept[Groom Recipient]		-5.9062151	1.021258	33.45	<.0001*
total humans[Groom Recipient]		0.60419887	0.1604264	14.18	0.0002*
Intercept[Hang]		-3.4626526	0.5849713	35.04	<.0001*
total humans[Hang]		0.187694	0.2073532	0.82	0.3654
Intercept[Not Visible]		-0.9158515	0.1862225	24.19	<.0001*
total humans[Not Visible]		0.35203714	0.0696868	25.52	<.0001*
Intercept[Other]		-7.0115111	1.4481919	23.44	<.0001*
total humans[Other]		0.71085044	0.1806613	15.48	<.0001*
Intercept[Rest - Sleep]		-2.0491431	0.2866187	51.11	<.0001*
total humans[Rest - Sleep]		0.25952368	0.0987496	6.91	0.0086*
Intercept[Rest - Still]		-1.703556	0.2215666	59.12	<.0001*
total humans[Rest - Still]		0.40532436	0.0739462	30.05	<.0001*
Intercept[Self groom]		-5.34457	1.6699724	10.24	0.0014*
total humans[Self groom]		0.09443149	0.6681153	0.02	0.8876
Intercept[Travel]		-1.709588	0.2321228	54.24	<.0001*
total humans[Travel]		0.34947804	0.0784157	19.86	<.0001*

For log odds of Drink/Vocalize, Feed/Vocalize, Groom/Vocalize, Groom Recipient/Vocalize, Hang/Vocalize, Not Visible/Vocalize, Other/Vocalize, Rest - Sleep/Vocalize, Rest - Still/Vocalize, Self groom/Vocalize, Travel/Vocalize