Dose Response Probit analysis

[#1]

Hi group,

I am trying to reproduce a simple dose response analysis that I had performed in SPSS. So in JMP i am using the "Fit model" module, selecting for Generalized linear models, binomial distribution and probit link.

I have three variables, number of assays performed (10 assays), number of assays with positive result and concentration (from 0 to 36)

0 10 2

1 10 4

2 10 9

6 10 16

8 10 25

9 10 36

0 10 0

I select  number of assays performed as "Y" variable, number of assays with positive result as "Freq" and concentration in logs as variable to model effects on. But when I hit run I get this message in the results:

"Warning: Hessian not positive definite. Singularity is likely due to a poor fit of the model, or linear dependencies among the model covariates. Fit and result are of questionable value"

And the analysis is not performed.

Can anyone share some comments?

Thanks,

Dave

[#2 · Accepted solution]

Dave,

Your "number of assays with positive result" needs to go in as a "Y" variable also. The Frequency role is for indicating how many times a row in the data table actually occurred. In this case, the GLM model expects the number of assays performed and the number of positive results as "separate" Y values. The analysis will link them together.

One thing you did not mention that is often done for this type of work is to take the log of the concentration. I did this in the model dialog shown above. Highlight the concentration model effect, click the transform button and choose log. Results are posted here.

Dan

[#3]

Thanks a lot DanO, that is a very clear answer. It is interesting that JMP knows they are linked.

Regarding the log transformation, yes I will take that into account (it was indeed mentioned in my original post, although pretty vague I must admit!)

Best,

Dave

[#4]

Dear DanO,

sorry for bothering you again, but changing the numbers to the demo, I seem to be getting wrong results. Please have a look at this dataset, with same variables but different numbers. For the three highest concentrations I get 100% positives

Number of positive results Number of assays performed Concentration

0 1140 0.01

241 1140 0.1

590 1140 0.5

963 1140 1

1134 1140 5

1140 1140 10

1140 1140 50

1140 1140 100

I run the Probit as you suggested

An after running I get a strange result which doesn't make sense to me. Instead of doing percentages of corrects on the Y, it seems to be doing something different. What am I doing wrong?

Thanks ever so much for your help

Dave

[#5]

Been following this thread with interest.

From the JMP docs:

If your data is summarized as frequencies of events and trials, specify two continuous

columns in this order: a count of the number of successes, and a count of the number of

trials. Alternatively, you can specify the number of failures instead of successes.

(my emphasis).

So if you switch the order the 2 y variables are entered I think you will see more of what you expected especially if you change the x axis to be logarithmic.

That said, I can't explain why the order doesn't seem to matter with your original data.

Michael

[#6]

The 0 10 0 last row from the original data for some reason insulates the analysis from needing the correct order. If you leave it out then order does matter.

Michael

[#7]

That is indeed the right order to feed in the variables. Thanks for pointing that out, Michael.

Dave