Calcite | Level 5

## correcting/ adjusting for overdispersion and underdispersion

Hello,

I am wondering how to correct for over - and underdisperion in glimmix. Could someone help me. Thanks!

Proc glimmix data = doc1;
ID Idn;
class diet strain;
model Thick = diet|strain / DDFM = KENWARDROGER;
random residual / subject = pen;
lsmeans diet|strain;
run;

The output is often:

Generalized Chi-SquareGener. Chi-Square / DF
 454.29 8.11

or

Generalized Chi-SquareGener. Chi-Square / DF
 6.44 0.11

1 ACCEPTED SOLUTION

Accepted Solutions
Diamond | Level 26

## Re: correcting/ adjusting for overdispersion and underdispersion

So, for my understanding. In this case the Chi-square/df does not really say something with this model.

The opposite is true. It gives you some measure of dispersion of the data around the fitted line.

--
Paige Miller
16 REPLIES 16
Diamond | Level 26

## Re: correcting/ adjusting for overdispersion and underdispersion

Calcite | Level 5

## Re: correcting/ adjusting for overdispersion and underdispersion

I tried it as the statement:

Proc glimmix data = Anu.organday1_3;
ID Idn;
class diet strain;
model Gizz_Thick_rel = diet|strain / DDFM = KENWARDROGER;
random residual / subject = pen;
random_residual_ = Gizz_thick_rel;
lsmeans diet|strain;
run;

However, it stays 8.11

Diamond | Level 26

## Re: correcting/ adjusting for overdispersion and underdispersion

Can you please show the entire output from PROC GLIMMIX instead of just a few lines?

Please click on the {i} icon and paste the output, as text, into the window that appears. Do not skip this step.

--
Paige Miller
Calcite | Level 5

## Re: correcting/ adjusting for overdispersion and underdispersion

```Proc glimmix data = Anu.organweightday123_3;
ID Idn;
class diet strain;
model Pancreas_rel = diet|strain / DDFM = KENWARDROGER;
random residual / subject = pen;
lsmeans diet|strain;
run;

```
```The SAS System

The GLIMMIX Procedure

Model Information
Data Set ANU.ORGANWEIGHTDAY123_3
Response Variable Pancreas_rel
Response Distribution Gaussian
Variance Function Default
Variance Matrix Blocked By Pen
Estimation Technique Restricted Maximum Likelihood
Degrees of Freedom Method Kenward-Roger

Class Level Information
Class Levels Values
diet 2 1 2
strain 2 A B

Number of Observations Used 60

Dimensions
R-side Cov. Parameters 1
Columns in X 9
Columns in Z per Subject 0
Subjects (Blocks in V) 30
Max Obs per Subject 3

Optimization Information
Optimization Technique None
Parameters 0
Lower Boundaries 0
Upper Boundaries 0
Fixed Effects Profiled
Residual Variance Profiled
Starting From Data

Fit Statistics
-2 Res Log Likelihood 280.34
AIC (smaller is better) 282.34
AICC (smaller is better) 282.42
BIC (smaller is better) 283.74
CAIC (smaller is better) 284.74
HQIC (smaller is better) 282.79
Generalized Chi-Square 403.67
Gener. Chi-Square / DF 7.21

Covariance Parameter Estimates
Cov Parm Estimate Standard
Error
Residual (VC) 7.2084 1.3623

Type III Tests of Fixed Effects
Effect Num DF Den DF F Value Pr > F
diet 1 56 0.00 0.9502
strain 1 56 1.49 0.2266
diet*strain 1 56 1.02 0.3177

diet Least Squares Means
diet Estimate Standard
Error DF t Value Pr > |t|
1 3.4287 0.4784 56 7.17 <.0001
2 3.4724 0.5074 56 6.84 <.0001

strain Least Squares Means
strain Estimate Standard
Error DF t Value Pr > |t|
A 3.0242 0.5074 56 5.96 <.0001
B 3.8768 0.4784 56 8.10 <.0001

diet*strain Least Squares Means
strain diet Estimate Standard
Error DF t Value Pr > |t|
A 1 2.6508 0.7176 56 3.69 0.0005
B 1 4.2065 0.6328 56 6.65 <.0001
A 2 3.3976 0.7176 56 4.73 <.0001
B 2 3.5472 0.7176 56 4.94 <.0001

```
Diamond | Level 26

## Re: correcting/ adjusting for overdispersion and underdispersion

Hmmm ... okay, are you saying that this represents over-dispersion? Why do you say that?

--
Paige Miller
Rhodochrosite | Level 12

## Re: correcting/ adjusting for overdispersion and underdispersion

As you ponder your answer to @PaigeMiller 's question, you can keep in mind that overdispersion is not an issue for the Gaussian distribution (which is what your model assumes). I think Paige may be trying to make you think about your understanding of the model and the output, and I am, maybe, giving you a hint.

We do consider the possibility of overdispersion for one-parameter distributions in the exponential family, like binomial and Poisson.

Rhodochrosite | Level 12

## Re: correcting/ adjusting for overdispersion and underdispersion

Let me also note that the reason that @PaigeMiller asks you for the actual code that you ran AND the actual output from that code is because the Community cannot assess your problem unless we have enough of the right details. If you look at your previous posts and compare them to your last post, you'll see that your model changes with each post. From our point of view, it is hard to hit a moving target. So thank you for taking Paige's advice.

Calcite | Level 5

## Re: correcting/ adjusting for overdispersion and underdispersion

Well after reading of different articles and of watching different YouTube movies, I thought that the generalized chii square/df should be near 1.

And I showed you in this case a different response variable, indeed one with Gaussian distribution.

So, I have different values of genre chi square/df, but with the same model and all not near one.

But you are saying that with the Gaussian distribution, this value is not a problem?
Diamond | Level 26

## Re: correcting/ adjusting for overdispersion and underdispersion

Yes, for Gaussian distribution (which is the default fit by GLIMMIX), there is no such thing as overdispersion. That doesn't mean the model fits well, there can be other problems, but not overdispersion.

You see Gaussian distributions are fit in such a way that the mean and the variance are estimated from the data. In other distributions, such as the Poisson or exponential, the variance is known before the model fit, and when the variance is estimated from the model fit is not close to the known variance, then you have underdispersion or overdispersion (example: if you have a Poisson distribution, the variance must be equal to the mean).

--
Paige Miller
Calcite | Level 5

## Re: correcting/ adjusting for overdispersion and underdispersion

Thank you for the explanation.

However, the question arises. What are the other problems or is it better to use an entire different model, like proc mixed.
Diamond | Level 26

## Re: correcting/ adjusting for overdispersion and underdispersion

As far as I know, for the Gaussian case, PROC MIXED and PROC GLIMMIX should produce the same results for the same model.

Other problems: poor model fit, which can happen even in non-Gaussian cases with no overdispersion.

But its not clear why you don't like this model that you have fit, what is wrong with it?

--
Paige Miller
Calcite | Level 5

## Re: correcting/ adjusting for overdispersion and underdispersion

So, for my understanding. In this case the Chi-square/df does not really say something with this model. However, if you would use the poisson distribution. Like for instance this example. Only in this case, the chi-square/df says something? Is there an article about this?

```The SAS System

The GLIMMIX Procedure

Model Information
Data Set ANU.ORGANDAY1_3
Response Variable Progizz_score
Response Distribution Poisson
Variance Function Default
Variance Matrix Blocked By Pen
Estimation Technique Residual PL
Degrees of Freedom Method Kenward-Roger

Class Level Information
Class Levels Values
diet 2 1 2
strain 2 A B

Number of Observations Used 60

Dimensions
R-side Cov. Parameters 1
Columns in X 9
Columns in Z per Subject 0
Subjects (Blocks in V) 30
Max Obs per Subject 3

Optimization Information
Optimization Technique None
Parameters 0
Lower Boundaries 0
Upper Boundaries 0
Fixed Effects Profiled
Residual Variance Profiled
Starting From Data

Iteration History
Iteration Restarts Subiterations Objective
Function Change Max
0 0 0 -12.50422765 0.30362060 .
1 0 0 -9.527888119 0.00779297 .
2 0 0 -9.480642908 0.00000395 .
3 0 0 -9.480626779 0.00000000 .

Convergence criterion (PCONV=1.11022E-8) satisfied.

Fit Statistics
-2 Res Log Pseudo-Likelihood -9.48
Generalized Chi-Square 7.82
Gener. Chi-Square / DF 0.14

Covariance Parameter Estimates
Cov Parm Estimate Standard
Error
Residual (VC) 0.1397 0.02639

Type III Tests of Fixed Effects
Effect Num DF Den DF F Value Pr > F
diet 1 56 3.88 0.0539
strain 1 56 1.64 0.2059
diet*strain 1 56 0.81 0.3705

diet Least Squares Means
diet Estimate Standard
Error DF t Value Pr > |t|
1 1.1795 0.03708 56 31.81 <.0001
2 1.2829 0.03719 56 34.50 <.0001

strain Least Squares Means
strain Estimate Standard
Error DF t Value Pr > |t|
A 1.1976 0.03886 56 30.82 <.0001
B 1.2648 0.03532 56 35.81 <.0001

diet*strain Least Squares Means
strain diet Estimate Standard
Error DF t Value Pr > |t|
A 1 1.1221 0.05699 56 19.69 <.0001
B 1 1.2368 0.04746 56 26.06 <.0001
A 2 1.2730 0.05285 56 24.09 <.0001
B 2 1.2928 0.05233 56 24.70 <.0001 ```

Diamond | Level 26

## Re: correcting/ adjusting for overdispersion and underdispersion

Maybe you could answer my questions that you haven't yet answered. Specifically:

"are you saying that this represents over-dispersion? Why do you say that?"

"its not clear why you don't like this model that you have fit, what is wrong with it?"

--
Paige Miller
Calcite | Level 5

## Re: correcting/ adjusting for overdispersion and underdispersion

Maybe just a misunderstanding, because i thought with the other post that you were saying that there was no overdispersion, but maybe that are different problems. So, I thought you meant that the model did not look good.

I am content with the model, but I was just confused by the high value of the chi square/df

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