# Need help with nested random/mixed effect model specification

I am a newbie in meta-analysis and I need your opinion on the design of my random-effect model.

I have conducted an experiment on the performance of a provider who has around 30-40 data centres. I picked two such data centres at random and monitored their performance for 7 consecutive weekdays. I took 2 measurements per day (1 during the peak and 1 during the off-peak). Now I have three factors in my experiment design: data centres, day and time having 2, 7 and 2 levels respectively. I want to know how much each of these factors contribute to the variance in performance. I have the following nested model in my mind:

m1 <- lme(Performance ~ 1, random =~ 1|DataCentre/Day/Time, data=mydata)


I am pretty sure that the time factor is nested within day; however, not quite sure whether the data centre should be a part of the nested structure. I assume that each data centre may have its own pattern of variability across different days, that's why included it in the nested structure.

Do you think this model is correct? Is there any other approach that you can suggest?

Thanks.

• Could you please suggest me whether the nested model is appropriate for my data? – sim May 20 '15 at 9:48
• I do not think so but I am not an expert at this. Why did you remove linear regression output? – rnso May 20 '15 at 10:26
• I removed those outputs because it wasn't formatted properly. – sim May 20 '15 at 13:52

Do not use a mixed model. Levels of a random factor should be exchangeable, this is the case only for datacenter. Day is problematic since there could be start/end of week effects. It is not even clear if the weekend is included? Looking at time, peak and off-peak are obviously not exchangeable.

You should also have more than two levels for a random factor. Two is not enough, so even datacenter should not be a random factor. Otherwise datacenter would be a very good candidate for being modelled as a random factor.

I hesitate to suggest any alternative analysis since when considering all three experimental factors and their interactions, you just have one sample per group. Is there any valid reason to pre-suppose that the performance does not depend on the exact combination of datacenter, peak/off-peak and day of week?

• Here is the answers to your questions: I took measurements for seven days, that is, Sun, Mon, Tue, Wed, Thu, Fri and Sat. I used a fixed-effect model for this data. I have found that the day-to-day variability is very low, however, the day:time interaction and datacenter impact is significant. What could be an alternative design to this? – sim May 20 '15 at 14:04

If you tested only 2 centers and only once at peak and off-peak hour on each day, the sample size is too small for day of week analysis.

I think you can use here linear regression with interactions of other variables:

lm(performance ~ DC * Time, data=mydata)


Edit: The orange price example in using-lsmeans vignettes is very similar to your data and you may find it helpful: http://cran.r-project.org/web/packages/lsmeans/vignettes/using-lsmeans.pdf

• Thanks for your solution. In fact, my question has been answered by both you and Erik. Tried to mark both as answer, but it doesn't allow multiple answers. – sim May 21 '15 at 1:42
• Please see my edit above. – rnso May 21 '15 at 2:13
• Thanks for the link. I believe I can use it to summarise my results. – sim May 22 '15 at 5:31