topic Re: Logistic regression with multiple outcome variables - Odds ratios in JMP in Discussions

Logistic regression with multiple outcome variables

melsie999 — Wed, 16 May 2012 22:45:44 GMT

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?

Re: Logistic regression with multiple outcome variables

Mark_Bailey — Thu, 17 May 2012 14:09:24 GMT

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.

Re: Logistic regression with multiple outcome variables

melsie999 — Thu, 17 May 2012 15:22:51 GMT

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.

Re: Logistic regression with multiple outcome variables

Mark_Bailey — Thu, 17 May 2012 15:55:37 GMT

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.

Re: Logistic regression with multiple outcome variables

plf515 — Thu, 17 May 2012 17:01:06 GMT

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?

Re: Logistic regression with multiple outcome variables

melsie999 — Thu, 17 May 2012 17:14:36 GMT

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

Re: Logistic regression with multiple outcome variables

Mark_Bailey — Thu, 17 May 2012 17:44:54 GMT

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.

Re: Logistic regression with multiple outcome variables

plf515 — Thu, 17 May 2012 18:05:13 GMT

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:

Re: Logistic regression with multiple outcome variables

melsie999 — Thu, 17 May 2012 18:18:24 GMT

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

Re: Logistic regression with multiple outcome variables

Mark_Bailey — Thu, 17 May 2012 18:26:53 GMT

Use the LRTs to judge signficance and choose your model. Once that part is done, then use the model to compute the odds ratios.

Use the prediction profiler to compute the probabilities and then the odds of an event versus the non-event for a given predictor level. Change the predictor level, get the updated probabilities, and compute the new odds. You can then compute the ratio. This way you can compute the odds ratio for anything.

Re: Logistic regression with multiple outcome variables

melsie999 — Fri, 18 May 2012 19:14:59 GMT

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.

Re: Logistic regression with multiple outcome variables - Odds ratios in JMP

jennifer_n_blak — Thu, 16 Mar 2017 01:15:24 GMT

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!

Re: Logistic regression with multiple outcome variables - Odds ratios in JMP

Mark_Bailey — Thu, 16 Mar 2017 13:30:06 GMT

The odds ratios are available in both the Logistic platform (starting with Fit Y by X) and the Nominal Logistic Fit platform (starting with Fit Model). Using the tutorial example that you cited above, I get this result using the first platform:

I get this result using the second platform:

Note that odds ratios are only available for a nominal response.

Re: Logistic regression with multiple outcome variables - Odds ratios in JMP

Mark_Bailey — Thu, 16 Mar 2017 13:38:38 GMT

I think I know what the problem is, The example that you cited has a binary outcome. It sounds, however, like your data has more than two levels. JMP does not compute the odds ratios in such a case. You can save the probability formulas, though, and compute the odds and then the odds ratios with them.

Re: Logistic regression with multiple outcome variables - Odds ratios in JMP

jennifer_n_blak — Thu, 16 Mar 2017 15:51:51 GMT

Dear Mark,

Thanks for your help! I certainly wish JMP did this automatically. Maybe in version 14 :)

When I save the prob formulas I get the following columns

Lin [F] Lin [B] Prob [F] Prob [B] Prob [M] Most likely outcome

Where F, B, and M are my outcomes and M is the reference category.

Questions:

What are the Lin[ ] columns telling me?

Computing this for binary logisitc regression wouldn't be all that hard, but here I think it is a bit trickier.

How do I

- compute the odds for each individual?

- compute the odds for each outcome category group?

Once I have the odds for each outcome group I simply divide these by the combined odds for the refernce group to get the odds ratios (of F compared to M, for example). Is that correct?

Thanks for sharing your statistical know-how!

Re: Logistic regression with multiple outcome variables - Odds ratios in JMP

Mark_Bailey — Thu, 16 Mar 2017 16:20:31 GMT

The Lin[X] columns contain the linear predictor for the logit function that you fit. If you examine the formula, you will see the same parameter estimates as were shown in the logistic regression results. You don't need it unless you need the logit!

The linear predictor is, n turn, used to compute the probability of each response level as Prob[X]. (It comes from solving log( p / (1-p) ) = Lin[X] for p.) This probability is most useful for your purpose. Note that if you select Graph > Profiler and select Prob[X], be sure to enable the feature to expand the intermediate formulas, otherwise you will profile against Lin[X] instead of the actual predictor variable.

You can use the Prob[X] columns in new column formulas to compute any odds that you want as Prob[X1] divided by Prob[X2]. Likewise, you can then compute any odds ratio that you want from the odds derived this way.

Re: Logistic regression with multiple outcome variables - Odds ratios in JMP

jennifer_n_blak — Thu, 16 Mar 2017 20:17:51 GMT

I see! Thank you!

A follow up~

When I use the Prob[X] columns to compute odds t(Prob[X1] divided by Prob[X2]) that will give me the odds for that individual, correct?

When I report this in a paper I will need to report the odds for each group and the odds ratio for compared groups (F treated compared to M treated or untreated, for exmaple).

When computing group odds do I simply average the odds for that group?

I realize this is more of a statistics question than for JMP per say, but most programs calculate group odds so I can't find other documentation on how to do it by hand. Thank you!

Re: Logistic regression with multiple outcome variables - Odds ratios in JMP

Mark_Bailey — Thu, 16 Mar 2017 20:37:34 GMT

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).

Re: Logistic regression with multiple outcome variables

irinastl — Tue, 11 Jul 2017 21:40:58 GMT

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

Re: Logistic regression with multiple outcome variables

irinastl — Tue, 05 Sep 2017 21:42:15 GMT

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