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Logistic regression with multiple outcome variables

melsie999

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?

Accepted answers

Mark_Bailey

If you have more than two levels in the response variables, then you are using ordinal or nominal logistic regression. In both of these cases, the cumulative logits or generalized logits, respecitvely, use the last level for the odds, so it cannot estimated. So if you have k levels, then there are k-1 logits with their associated parameters.

The best way to interpret these logits is either by odds ratios (relative to the last level) or with a specific visualization, such as the prediction profiler in JMP.

Mark_Bailey

I must admit that I do not know the subset of JMP features that are available in the student version, but please try these suggestions and let me know what you find.

1. Using Fit Y by X, you launch a Logistic platform. You already foiund the p-values for the Wald tests to judge significance. Click the red triangle at the top of the window and select Odds Ratios. Two of them appear to the right of the parameter estimates and the p-values. The Unit Odds Ratio is the ratio for 1 unit change in the predictor. The other Odds Ratio is for the change over the whole range (minimum to maximum) of your predictor.

(Note: if you launch Logistic with multiple responses, you will get parallel models in the same window. Try this: press and hold the CTRL on Windows or Command on Macintosh, and then click the red triangle. This way the odds ratios will be computed for all of the responses, instead of asking one response at a time. This trick is called broadcasting and works with most features in JMP!)

2. Alternatively, select Analyze > Fit Model. Assign your responses to the Y role and add your predictor to the effects list. Click the Run button and you should get the same basic analysis as you did from Logistic, but with importance differences. The parameter estimates use likelihood ratio tests instead of Wald tests. Also, click the red triangle at the top and select Profilers > Profiler. It will appear at the bottom of the window. Now the profiler shows you the predicted probabilities of each response level. You can estimate the probabilities under some reference level of the predictor, then estimate the probabilites under other conditions and form any odds ratio that you might need.

There are many more features in the Logistic and the Nominal Logisitic Fit platforms, but I don't want to overwhelm you all at once. Please let me know if this explanation was helpful, or if you have any more difficulty or questions.

All comments

Mark_Bailey

The best way to interpret these logits is either by odds ratios (relative to the last level) or with a specific visualization, such as the prediction profiler in JMP.

melsie999

Thanks for the help. I have a student license of JMP. I cannot find the odds ratio test and I cannot figure out how to use the profiler with non-numeric values. Do you know how I can access these functions? I just am running a fit y by x analysis, so I also do not know how to indicate I am running a nominal logistic regression.

Mark_Bailey

I must admit that I do not know the subset of JMP features that are available in the student version, but please try these suggestions and let me know what you find.

plf515

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?

melsie999

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

Mark_Bailey

The Nominal Logistic Regression personality in Fit Model should help. You can get the odds ratios by clicking on the red triangle at the top of the platform. Also, you can use the prediction profiler to estimate the probability of all the levels for any condition, and then compute the odds. Now change the condition (predictor level) and repeat the calculation. Now compute the odds ratio.

plf515

The fact that two parameter estimates are unstable indicates that DRINK was probably an uncommon behavior.

The easiest way to interpret logistic regression is via odds ratios - which are exp(parameter estimate) and predicted probabilities. I don't know JMP, but if you have SAS/STAT I wrote a paper on multinomial logistic. It's here:

melsie999

Can you give me more information on the predictor profiler? I am able to get that figure when I run the test with fit model instead of fit y by x, but I am not sure how to estimate the odds for each prediction. What I got was a figure like the one I made, but with red horizontal lines on it as well. There are several options in the red drop down arrow, but I am not sure which one tests each prediction. And indeed, drink was a rare behavior, I assumed that is why it was unstable.

I am having a problem running the odds ratio in that jmp won't give me that option because there are more than 2 behaviors. I think that is what I need to do, but I can't seem to make jmp do it. The option does not appear on the drop down triangle unless I make up a new data sheet that only has 2 possible outcomes in the response variable. I can use the predictor profiler, but I am not really familiar with how it works.

Thanks again

melsie999

As an update, this is what I am doing now: I am running each behavior individually using a standard binomial logistic regression, scoring behaviors as 1 for when they occurred and 0 for all other behaviors (only when the nominal logistic regression was significant). I am only doing this for common behaviors. This ends up being what I wanted to compare (one behavior vs. all other over number of people). The only issue I am having now is whether or not I need to do a correction for running multiple tests (such as bonferroni). I am running only 5 behaviors (feed, not visible, sleep, rest, travel, vocalize), so I am not sure if the correction is needed. I know bonferroni can be a little conservative, so I am a little hesitant to use it unless it seems really necessary.

jennifer_n_blak

I am running a multiple multinomial logisitc regression and am unable to get JMP to compute the odds ratios as is shown in tutorials using canned data sets.

Following the above instructions:

When I use fit Y by X (broadcasted or not) the odds ratio option does not come up (see first and second screen shots below).

I can find the profiler, but I am really looking for odds ratios so that I can compare them to ones I already computed by hand (see third screen shot on right).

Has anyone else had this problem? Were you ever able to get JMP to compute odds ratios for a multiple multinomial logistic?

Thanks for your help!

JMP odds ratio output question.png

irinastl

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

irinastl

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

Mark_Bailey

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.

mrosenthal

A bit of a simplistic GUI based solution: in the parameter estimates table I double clicked the table. I chose the "Make into Data Table" option. Once JMP produced the data table I created a new column which I named odds ratio. Then I chose the formula option in the Cols menu. Once inside the formula window I wrote the formula: exp(Estimate). The output was the odds ratio for the estimates. To double check, I copy pasted the estimates into R and used the exp function in R. It gave the same results. HTH