# [R] Gaussian glm for grouped data with unequal variances

Chuck Cleland ccleland at optonline.net
Tue Jan 16 12:51:25 CET 2007

```Dawn Ashcourt wrote:
> Hello - I am fairly new to R, (i.e., ability to create functions/write
> programs insignificant) and was wondering if there might be a convenient way
> to model the following: I want to fit a gaussian glm to grouped data, while
> allowing for unequal variances in each of the groups.
> More specifically, my data set looks something like this:
> ----------------
>    data group
> 1    76     1
> 2    82     1
> 3    83     1
> 4    54     1
> 5    35     1
> 6    46     1
> 7    87     1
> 8    68     1
> 9    87     2
> 10   95     2
> 11   98     2
> 12  100     2
> 13  109     2
> 14  109     2
> 15  100     2
> 16   81     2
> 17   75     2
> 18   68     2
> 19   67     2
> 20  105     3
> .... et cetera.
> ---------------
> There are seven groups in all, each with a different number of observations.
> The idea is to compare a model in which all the data points can be modeled
> with a single mean (i.e., if all the group means are equal), or if the  data
> suggests that each of the groups has a different mean. In other words, I
> want to do a Likelihood ratio test on whether or not the group means are
> significantly different from each other: the full model would be glm(data ~
> as.factor(group)-1, family = gaussian), to be compared against a restricted
> model that only includes an intercept. However, I also need to allow for the
> fact that each group has a different variance. And this I have no idea how
> to do. I would really appreciate some help in this matter.

Have you considered oneway.test()?  For example:

## Not assuming equal variances
oneway.test(breaks ~ tension, data = warpbreaks)

One-way analysis of means (not assuming equal variances)

data:  breaks and tension
F = 5.8018, num df = 2.00, denom df = 32.32, p-value = 0.007032

> Dawn.
>
> 	[[alternative HTML version deleted]]
>
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> and provide commented, minimal, self-contained, reproducible code.

--
Chuck Cleland, Ph.D.
NDRI, Inc.
71 West 23rd Street, 8th floor
New York, NY 10010
tel: (212) 845-4495 (Tu, Th)
tel: (732) 512-0171 (M, W, F)
fax: (917) 438-0894

```