topic Re: GLIMMIX 0 Standard Error Infinity t value in Statistical Procedures

GLIMMIX 0 Standard Error Infinity t value

Nerdcy — Sat, 04 Jul 2020 22:29:31 GMT

Hi everyone,

I'm running into some issue with my data. I'm using GLIMMIX to model a growth curve analysis on longitudinal data. My code is below:

proc glimmix data=diss method = LAPLACE;
title Total Support Conditional Growth Model;
class carnegie (Ref='0') barrons (Ref='0')flagship(Ref='0');
model totalsupport =
time time*time carnegie barrons flagship stateGMC unemploymentGMC disposableGMC
time*carnegie time*barrons time*flagship time*stateGMC time*unemploymentGMC time*disposableGMC
time*time*carnegie time*time*barrons time*time*flagship time*time*stateGMC time*time*unemploymentGMC time*time*disposableGMC
time*carnegie*stateGMC time*barrons*stateGMC time*flagship*stateGMC time*unemploymentGMC*stateGMC time*disposableGMC*stateGMC
time*time*carnegie*stateGMC time*time*barrons*stateGMC time*time*flagship*stateGMC time*time*unemploymentGMC*stateGMC time*time*disposableGMC*stateGMC
/dist=Gamma link=log solution;
random intercept time / type=AR(1) subject = id;
covtest/Wald;
run;

A sample of my output looks like this:

Solutions for Fixed Effects

Estimate StandardError DF t Value Pr > |t|
Intercept 7.7140 0.09218 373 83.68 <.0001
time 0.05337 0.06763 367 0.79 0.4305
time*time -0.00134 0.001119 3904 -1.19 0.2326
carnegie 1 -0.6266 0.06365 3904 -9.84 <.0001
carnegie 2 -0.6237 0.1218 3904 -5.12 <.0001
barrons 1 0.4344 0.07189 3904 6.04 <.0001
barrons 2 -0.2856 0.08835 3904 -3.23 0.0012
flagship 1 -0.6660 0.08558 3904 -7.78 <.0001
stateGMC 0.000048 0.000021 3904 2.33 0.0197
unemploymentGMC -0.1080 0.02829 3904 -3.82 0.0001
disposableGMC -0.00003 0 3904 -Infty <.0001
time*time*disposable -1.62E-7 0 3904 -Infty <.0001
time*stateGM*carnegi 1 1.028E-6 0 3904 Infty <.0001
time*stateGM*carnegi 2 -6.91E-8 0.000016 3904 -0.00 0.9966
time*stateGM*barrons 1 -2.99E-6 0 3904 -Infty <.0001
time*stateGM*barrons 2 -1.17E-6 0 3904 -Infty <.0001
time*stateGM*flagshi 1 4.32E-6 0 3904 Infty <.0001
time*stateGM*unemplo -1.08E-8 0 3904 -Infty <.0001
time*stateGM*disposa -565E-13 0 3904 -Infty <.0001
time*time*stat*carne 1 -1.56E-7 0 3904 -Infty <.0001
time*time*stat*carne 2 -1.06E-7 0 3904 -Infty <.0001
time*time*stat*barro 1 2.987E-7 0 3904 Infty <.0001
time*time*stat*barro 2 2.956E-7 0 3904 Infty <.0001
time*time*stat*flags 1 -2E-7 0 3904 -Infty <.0001
time*time*stat*unemp 2.46E-8 0 3904 Infty <.0001
time*time*stat*dispo 4.23E-13 . . . .

Basically, any fixed effects with either stateGMC (grand mean-centered continuous variable) or disposableGMC (grand mean-centered continuous variable) gives me a standard error of 0 or . and Infinity for the t value. Obviously this is wrong and doesn't make sense.

I checked the multicollinearity of these variables (also checked the correlation matrix) but they look fine.

Variable DF Parameter Estimate Standard Error t Value Pr > |t| Tolerance Variance Inflation
Intercept 1 3965.76565 85.20213 46.55 <.0001 . 0
time 1 57.24893 5.92625 9.66 <.0001 0.85547 1.16895
carnegie 1 -661.36628 39.82289 -16.61 <.0001 0.85578 1.16853
barrons 1 124.55068 30.89715 4.03 <.0001 0.96042 1.04121
flagship 1 -2832.86619 78.96505 -35.87 <.0001 0.80615 1.24047
stateGMC 1 0.10810 0.00542 19.93 <.0001 0.89349 1.11921
unemploymentGMC 1 -45.76003 12.24164 -3.74 0.0002 0.91471 1.09324
disposableGMC 1 -0.05768 0.00469 -12.30 <.0001 0.70785 1.41272
gdpGMC 1 3.61928E-10 4.01861E-11 9.01 <.0001 0.77164 1.29594

Can anyone point me to some other issues it could be?

Re: GLIMMIX 0 Standard Error Infinity t value

PaigeMiller — Sun, 05 Jul 2020 10:50:02 GMT

Some of these variables with 0 standard error are (within roundoff error) completely correlated with (linear combinations of) other variables;
Or there is no variability in the response variable after accounting for the effects of other variables; the terms in the model with 0 variability have no explanatory power; all of the variability is explained by the terms with the standard error > 0.

Basically, any fixed effects with either stateGMC (grand mean-centered continuous variable) or disposableGMC (grand mean-centered continuous variable) gives me a standard error of 0 or . and Infinity for the t value. Obviously this is wrong and doesn't make sense.

My general rule here is that when SAS says one thing and the user says it is wrong, I believe SAS.

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Re: GLIMMIX 0 Standard Error Infinity t value

sld — Sun, 05 Jul 2020 23:51:43 GMT

A potpourri of ideas:

You don't say which variables you checked for multicollinearity, and it's not clear that you centered all continuous covariates (i.e., time and unemploymentGMC). Quadratic terms can easily be collinear, e.g., time and time*time. So I would try centering all continuous covariates.

In fact, I would rescale predictor variables; as you try to sort this out, use standardized continuous covariates (not just centered).

I'd start small and build up. No one wants to try to interpret 4-way interactions anyway 🙂

You have random linear slopes with time, but not time*time, or any other covariate. I'd start with just random intercept.

Are your covariates measured at the id-level or at the id-time-level? Does your model reflect the appropriate design structure?

Your Parameter Estimate table reports gdpGMC, but it's not in your model statement. It's difficult for the Community to sort out problems when the evidence is inconsistent and incomplete.

I hope this helps move you forward.

Re: GLIMMIX 0 Standard Error Infinity t value

PaigeMiller — Mon, 06 Jul 2020 10:27:31 GMT

You don't say which variables you checked for multicollinearity

It's not enough to check variables for multicollinearity. You also have to check linear combinations of variables with other linear combination of variables.

I also suspect centering might be a problem. I recall a case a long time ago where the centering was not exact and the slight roundoff error caused by the centering produced similar results.

Re: GLIMMIX 0 Standard Error Infinity t value

Nerdcy — Mon, 06 Jul 2020 14:33:15 GMT

Thank you for your response and informing me how to format my output.

Re: GLIMMIX 0 Standard Error Infinity t value

Nerdcy — Mon, 06 Jul 2020 14:34:10 GMT

Thank you. I will try centering time.

Re: GLIMMIX 0 Standard Error Infinity t value

Nerdcy — Mon, 06 Jul 2020 14:35:09 GMT

Thank you. I will try centering time which is the only variable I haven't centered.

Re: GLIMMIX 0 Standard Error Infinity t value

SteveDenham — Mon, 06 Jul 2020 17:24:10 GMT

In addition to all that @sld and @PaigeMiller offered, I will suggest some other ideas to consider - your subject is id. Be sure this is numeric for all subjects, and it wouldn't hurt to sort the dataset by id, as it is not in the CLASS statement. Next, your model cries out for the use of the EFFECT statement. If you added this:

EFFECT poly = polynomial(time/degree=2);

and changed the MODEL statement to:

model totalsupport =
poly carnegie barrons flagship stateGMC unemploymentGMC disposableGMC
poly*carnegie poly*barrons poly*flagship poly*stateGMC poly*unemploymentGMC poly*disposableGMC
poly*carnegie*stateGMC poly*barrons*stateGMC poly*flagship*stateGMC poly*unemploymentGMC*stateGMC poly*disposableGMC*stateGMC
/dist=Gamma link=log solution;

you would automatically center and scale time and time*time. I would really consider dropping the last line of effects in the MODEL statement (although that is a preference from biology, not economics). Multi-dimensional response surfaces are often indistinguishable from noise, and suffer from interpretability. For instance, suppose the time*time*carnegie*stateGMC is significant. What does that mean? Oh, and how many levels do carnegie, barrons and flagship have? If each is a binary, consider creating a catch-all variable (call it source for now), such that source has 3 levels -'Carnegie', 'Barrons' and 'Flagship'. If that is the case your model statement would become:

model totalsupport =
poly source stateGMC unemploymentGMC disposableGMC
poly*source poly*stateGMC poly*unemploymentGMC poly*disposableGMC
poly*source*stateGMC poly*unemploymentGMC*stateGMC poly*disposableGMC*stateGMC
/dist=Gamma link=log solution;

Just some thoughts.

SteveDenham

Re: GLIMMIX 0 Standard Error Infinity t value

sld — Mon, 06 Jul 2020 18:06:21 GMT

@SteveDenham Oh, good spotting about ID not being the CLASS statement! I like the EFFECT suggestion as well.

As Steve notes, ID can be omitted from the CLASS statement as long as the dataset is sorted by ID. Or I'm guessing that there are about 400 subjects, so ID could go into CLASS; you'd probably want to turn off the classification table in the output. I think this would work:

ods exclude classlevels;

The DO Loop: What is the best way to suppress ODS output in SAS?

The GLIMMIX Procedure ODS Table Names

Re: GLIMMIX 0 Standard Error Infinity t value

SteveDenham — Mon, 06 Jul 2020 18:15:17 GMT

In addition to @sld 's method for suppressing huge class level lists, there is a NOCLPRINT option for the PROC GLIMMIX statement.

SteveDenham

Re: GLIMMIX 0 Standard Error Infinity t value

sld — Mon, 06 Jul 2020 18:17:37 GMT

Even easier!

Re: GLIMMIX 0 Standard Error Infinity t value

Nerdcy — Tue, 07 Jul 2020 20:53:54 GMT

Thank you! I will use effect poly.

Re: GLIMMIX 0 Standard Error Infinity t value

Nerdcy — Tue, 07 Jul 2020 20:56:30 GMT

Hi, after centering time it still didn't work, but when I used the log of the predictors it worked fine. Does this mean it was not a linear relationship (logged outcome and logged predictor)?

Re: GLIMMIX 0 Standard Error Infinity t value

Nerdcy — Tue, 07 Jul 2020 20:57:11 GMT

Hi, as an update, after centering time it still didn't work, but when I used the log of the predictors it worked fine. Does this mean it was not a linear relationship (logged outcome and logged predictor)?

Re: GLIMMIX 0 Standard Error Infinity t value

sld — Tue, 07 Jul 2020 21:06:40 GMT

Nonlinear relationships are certainly a possibility. At a minimum, when you have a model that runs, you would do the usual regression diagnostics and residual analyses.

It could also be that the log transformation rescaled the variables, reducing their variances or making their variances more similar. Have you tried standardizing?

Did you address the issue with ID and either sorting or including it in the CLASS statement?

Re: GLIMMIX 0 Standard Error Infinity t value

Nerdcy — Wed, 08 Jul 2020 15:42:31 GMT

Yes, after fixing the issues of ID and CLASS I'm still running into the same issues. I have attached my residuals (which actually look the same whether I use the logged predictors or not).

Re: GLIMMIX 0 Standard Error Infinity t value

sld — Wed, 08 Jul 2020 19:29:42 GMT

At this point, I don't know what model you are now running or what "the same issues" are. Presumably the model with log transformed predictors (all predictors? all predictors except time? transformed and then centered? transformed and then standardized?) appears to run without apparent errors? If you would like more input, provide us with an update of your model and your output.

Re: GLIMMIX 0 Standard Error Infinity t value

Nerdcy — Fri, 10 Jul 2020 14:45:55 GMT

Sorry for the confusion.

The model with the logged continuous predictors (not including time) works fine. I guess my question is more statistical in nature. My professor didn't want me to standardize these variables (which also worked) because it makes the random effects difficult to interpret. I guess my question is if I log the predictors, would that also make the random effects difficult to interpret or would I just follow the usual rules for interpreting after a log transformation?

Re: GLIMMIX 0 Standard Error Infinity t value

sld — Fri, 10 Jul 2020 16:42:24 GMT

I am puzzled by many aspects of your response, and I wonder if you meant to write about interpreting fixed effects rather than random effects.

With a model such as yours, I would say that we generally are not interested in interpreting the random effects, other than evaluating (either formally or informally) whether the variances/covariances are different than zero.

The scale of the random effects is determined by the scale of the response, not the scales of the predictors. With a gamma distribution and a log link, (co)variances are on the log scale.

We are, of course, interested in interpreting the fixed effects, and then the scales of both response and predictors do matter. Transformations and/or links (here, log for the gamma) change the fundamental form of the relationship between response and predictor; if you are fitting a linear regression model (including a generalized linear mixed model), then some combinations of scales for response and predictors may better meet the assumptions of linearity. Rescaling, such as centering or standardizing, does not affect the form of the relationship.

As personal rules of thumb: Ideally, I would only transform predictors to better meet linearity assumptions, or for some other "sensible" reason. For example, if one of my predictors is a pre-treatment/baseline measure of the same variable as the response, I transform the predictor to match the scale of the response. (I do not think you have a baseline predictor here.)

As for rescaling (as distinct from transformation), I generally center continuous predictors in regression, and I always center continuous predictors in regression when the predictors are involved in interaction. If I am having estimation trouble, or if I want to interpret predictor effects relative to a one standard deviation change, I standardize continuous predictors. Rescaling does not present any complicated challenges to interpretation.

I hope this helps move you forward.

If you have a professor, then you are at an institution where you might be able to find a statistician to provide more intensive help.

Re: GLIMMIX 0 Standard Error Infinity t value

SteveDenham — Mon, 13 Jul 2020 18:39:13 GMT

That Q-Q plot tells me that the link you have (or the distribution) isn't quite appropriate, as the residuals get much larger than expected as you move to higher quantiles. You may need to do something about the skewness of the residuals.

SteveDenham