topic Re: Multiple indicator responses and multiple continuous predictors in Discussions

Multiple indicator responses and multiple continuous predictors

gchesterton — Mon, 14 Aug 2023 18:03:16 GMT

Hi again, I'm using JMP Pro 15.2.1. I have a dataset where each observation has three continuous predictors and five indicator (y/n) responses. For each observation, any or all of the indicators may be present. I want to model the simultaneous effects of several predictors on a multidimensional response variable.

I can't seem to find the correct approach to this data. JMP balks at multiple categorical responses or the fact that my predictors are continuous.

Re: Multiple indicator responses and multiple continuous predictors

Phil_Kay — Thu, 17 Aug 2023 08:46:08 GMT

Hi @gchesterton ,

I might be misunderstanding what you are trying to do but this should not be a problem in JMP.

Analyze > Fit Model.

Specify your 5 binary responses in the Y role.

Add your 3 continuous predictors to the Construct Model Effects outline.

Run.

Is that what you have tried? If so, what was the problem?

It always helps if you can attach an illustrative example .jmp data table. Please no sensitive data though.

I hope this helps,

Phil

Re: Multiple indicator responses and multiple continuous predictors

gchesterton — Thu, 17 Aug 2023 13:24:12 GMT

Thanks @Phil_Kay , your proposed approach is precisely what I did and what I expected to work. But JMP is telling me that I can include only one nominal response. As you might guess, my nominal responses are each in their own columns. Obviously I could stack them into a single data column and add a source label column.

Re: Multiple indicator responses and multiple continuous predictors

Phil_Kay — Thu, 17 Aug 2023 13:41:16 GMT

I'm not able to replicate that behaviour.

Again, attaching example data to illustrate the query would really help.

Phil

Re: Multiple indicator responses and multiple continuous predictors

gchesterton — Thu, 17 Aug 2023 14:12:11 GMT

I've attached a comma separated text file. This is actual raw data with the headers changed. The predictors should be standardized/transformed but I don't think that's the issue at the moment.

Re: Multiple indicator responses and multiple continuous predictors

gchesterton — Thu, 17 Aug 2023 14:52:10 GMT

@Phil_Kay in addition to that dataset, here's my dialog in JMP.

Re: Multiple indicator responses and multiple continuous predictors

Mark_Bailey — Thu, 17 Aug 2023 15:08:08 GMT

I opened the CSV file in the current release, JMP Pro 17.2, and changed the modeling type of all Y columns to Nominal. I completed the Fit Model launch dialog as you indicated. I received the following results without any errors:

(Note that the report for the first four Ys is closed for sake of space.)

Re: Multiple indicator responses and multiple continuous predictors

Phil_Kay — Thu, 17 Aug 2023 15:28:15 GMT

Hi, @gchesterton .

I still can't reproduce your problem. Maybe because I am on JMP Pro 17.1.0 on Windows?

I suggest you contact tech support (support@jmp.com).

In any case, it is probably good to understand that what you will get from Fit Model will, in fact, be separate models for each response, but all in one JMP report window. So you could work around your issue by fitting each model separately - the models will be the same.

Re: Multiple indicator responses and multiple continuous predictors

gchesterton — Thu, 17 Aug 2023 16:09:27 GMT

Indeed I can produce a separate model for each nominal response. But my motivation for inserting all five response variables in the response window was not to simplify the process of doing five separate models. Instead, my thought is that I'm dealing with a multi-dimensional response. These responses are not independent, so I thought by including multiple response variables in a single model fit that it would recognize them as a multivariate response. In other words, the joint state of Y1-5 with predictors X1,2,3.

I could model Y1 ~ X1+X2+X3 + Y2+Y3+Y4+Y5 but I think what I really want is Y1 + ... + Y5 ~ X1 + X2 + X3.

Re: Multiple indicator responses and multiple continuous predictors

Phil_Kay — Fri, 18 Aug 2023 10:15:51 GMT

Makes sense, @gchesterton . You want to simultaneously understand the effects of X1 ... X3 on all responses Y1 ... Y5.

We could get very philosophical about what you mean by "responses are not independent" and we could explore sophisticated modelling techniques that treat Y1 ... Y5 as some kind of grouped, multivariate response.

But the pragmatic approach that people will use 99% of the time is to build separate models for each of Y1 ... Y5 against X1 .... X3 and then profile them together:

These are still separate models.

The process to do this is to save the Probability Formula for each model:

And then add the Prob[1] prediction formula column to Y, Prediction Formula role in Graph > Profiler.

I hope this helps,

Phil

Re: Multiple indicator responses and multiple continuous predictors

statman — Fri, 18 Aug 2023 15:37:18 GMT

I've been following this discussion, and I admit the information you've provided is too vague to provide any specific advice. It is very hard to give advice without appropriate context and unfortunately, as is often the case on a forum like this, it can be difficult to provide the appropriate context. Here are my thoughts which may not be helpful at all:

I'm not really sure what you mean by a "multidimensional response"? You later indicate these are "multivariate responses" which simply means you have multiple response variables. You suggest they are not independent, how did you determine this? It would be nice to know how the 5 nominal responses correlate, but that may not be possible to assess. I'm wondering if you can create a response variable that is a function of the 5 nominal responses? Perhaps an ordinal scale instead of a nominal response?

Re: Multiple indicator responses and multiple continuous predictors

gchesterton — Fri, 18 Aug 2023 16:36:06 GMT

As stated in the OP, each observation has 3 continuous predictors and 5 indicator responses. The state of Y1 (1 or 0) depends, in part, on the states of Y2-5. That's because humans are doing the indicating of each of the Y1-5 in each case. Their tendency to indicate Y2 = true, for example, will be influenced, in part, by their indication of Y1 and the other Ys.

It seems to me that if I model Y1 ~ X1 + X2 + X3 then I am ignoring information coming from the states of Y2-5. The response variable is a vector. I want to know how each predictor affects that vector.

Re: Multiple indicator responses and multiple continuous predictors

statman — Fri, 18 Aug 2023 17:31:20 GMT

You can ignore me, but I'm even more confused. I don't understand "states of Y2-Y5"? Are these different characteristics of the "sample"? Are humans "observing" a sample and determining 0 or 1? What does 0 and 1 mean? Arte these operationally defined (per Deming)?

If the response is a vector, why don't you quantify magnitude and direction?

If the response is a categorical response from human sensory perception, I would try to create more categories and use ordinal scales. If you are concerned with human bias, make sure the scale is a comparison scale not based on emotion. I would add repeated measures both within human and between human (same "sample" measured at least twice by same human and them other humans). You can use simple plots to see if there consistent biases from a particular human(s) and you can use averaging to reduce each of those components of variation.

Re: Multiple indicator responses and multiple continuous predictors

gchesterton — Fri, 18 Aug 2023 18:01:56 GMT

It's a vector in the mathematical sense -- that there is a list of values rather than a single element.

I'm not sure how else to describe a set of 5 indicator values.

In each observation, an assessor is indicating for each of 5 questions, whether it was true or false (on or off, 1 or 0). It's a basic binary indicator. What is not understandable about a binary indicator response???

The values are judgements by people who are assessing each of 5 possible 'reasons' in each observation. Each of the five responses can be yes or no, without exclusion of the others being yes or no. So, theoretically, the response vector could take on 32 different combinations.