# Exploring effect of treatment on count data

I've collected data on animal visitation at four different points in time. The four time points represent the total animal visitations over a three day period, i.e. 3 days of monitoring at four different times. The first two monitoring times there was no treatment applied to the visitation sites, while on the last two there was an artificial attractant used as a lure. An example of my dataset is below.

SITE    TREATMENT   TOTAL.VISIT    TIME
1           N             2        Sep13
2           N             1        Sep13
3           Y             2        Mar14
4           Y             2        Mar14
.
.
.
1           N             2        Sep14
2           N             1        Sep14
3           Y             3        Mar15
4           Y             4        Mar14


So, I've got repeated measures at multiple sites, pre- and post-treatment. I'm not interested in the actual sites themselves, but more the effect of the attractant (TREATMENT) and season (TIME). Even though the data suggests that (for example) site 1 received the treatment for Sep13, it did not - its there purely so I can look for differences between sites that would eventually receive the treatment.

My idea (I haven't done anything remotely like this since my undergrad days ~ 10 years ago), was to use a NB GLM (the real data contains lots of zeros, and the conditional variances >> conditional means) to assess the effects of treatment and season in the pre-treatment (Sep13, Mar14) data, and then assess them again in the post-treatment (Sep14, Mar15). That is, create two "independent" NB GLM models. The idea being that there should be no differences in TREATMENT for the first monitoring period (maybe difference in TIME); while for the last two monitoring periods there should (ideally) be a difference in TREATMENT and not in TIME.

Is my method statistically valid, or should I be using some sort of time series or repeated measures design?

• If your data contains lots of zeros, you may want to consider zero-inflated, hurdle, or zip models. You should consider employing a mixed model to address the repeated measures, and nested/clustering correlation effects found in your data. – StatsStudent Apr 17 '15 at 4:28
• @StatsStudent re:the repeated measures model - even if I'm not interested in the sites themselves? I'm only interested in the effects of (if any) TREATMENT and TIME on TOTAL.VISIT. – KaanKaant Apr 17 '15 at 5:11

If you are only interested in effect of Treatment and season on total visits, you would need to split time into month and year. The would look like:

SITE    TREATMENT   TOTAL.VISIT    MONTH YEAR
1           N             2        Sep  13
2           N             1        Sep  13
3           Y             2        Mar  14
4           Y             2        Mar  14
1           N             2        Sep  14
2           N             1        Sep  14
3           Y             3        Mar  15
4           Y             4        Mar  14
...


Then following is likely to give correct results:

aov(TOTAL.VISIT~ TREATMENT + MONTH + Error(SITE/TREATMENT:MONTH), data=mydata)

• I was under the impression that because I'm using counts (TOTAL.VISIT consists of counts), that ANOVA wasn't an appropriate method? That's why I was looking to use a negative binomial GLM. – KaanKaant Apr 18 '15 at 4:36
• Then why not keep it simple poisson with: glm(formula = total.visits ~ treatment*month, family = "poisson", data = mydata) – rnso Apr 18 '15 at 6:47