Poisson Regression for a
Field Ecology Study

RESEARCH QUESTION

What the Study Set Out to Compare

This Poisson regression example follows an ecology research team that wants to compare grassland bird counts between restored and unrestored sites. The counts come from point-count surveys, and the surveys were not all the same length: some points were observed for 5 minutes and others for 10.

The hypothesis is that restored sites have a higher rate of bird detections per minute of survey. Because sites were not assigned to restoration at random, the question is framed as an association, and the analysis describes the difference as a rate ratio with its uncertainty, not as the effect of restoration.

STUDY DESIGN AND DATA

Counts Nested in Sites, Observed for Unequal Time

Around 300 survey points nested within about 60 sites, roughly half restored and half unrestored. The dataset holds the bird count at each point, the minutes of survey, restoration status and site-level covariates such as site area and surrounding land cover. Points within a site resemble each other, so they are not independent observations, and the exposure time differs between points.

METHOD AND ASSUMPTIONS

Why Poisson With an Offset, and What Must Hold

Counts are non-negative integers, so a Poisson model with a log link is the natural starting point, and the log of survey minutes enters as an offset so that coefficients describe rates per unit of time and not raw counts. Because points within a site are correlated, standard errors are clustered by site, with a small-sample correction given the modest number of sites. The covariates and the clustering rule are fixed in the analysis plan before the counts are summarized.

The Poisson model assumes the variance of the count is close to its mean after adjustment, and real ecological counts are often more variable than that. Because the standard errors are cluster-robust, inference on the rate ratio does not rely on the variance equaling the mean, so the dispersion statistic is reported but not used to switch the primary model after the results are seen. A negative binomial model is prespecified as a sensitivity analysis, and the two sets of rate ratios are compared. Excess zeros are checked by comparing observed with predicted zeros, and a zero-inflated model is considered only if there is an ecological reason for structural zeros.

OUTPUT AND INTERPRETATION

What the Analysis Reports

The main output is the rate ratio for restored versus unrestored sites with its 95% confidence interval, explained in plain language as the proportional change in expected detections per minute of survey. A model table gives the rate ratios for the site covariates, and a figure shows the predicted count per 10-minute survey in each group, with intervals.

The interpretation covers the dispersion statistic, the comparison with the negative binomial model, and what happens to the rate ratio if the clustering approach changes. The write-up states what an association from non-randomized sites does and does not support, and notes that residual differences between sites, such as habitat quality before restoration, may account for part of any gap.

REPORTING

What the Researcher Received

A written report with statistical wording for the methods, matched to the output, for the team to check and incorporate, formatted to the target journal's requirements, with the model specification, the offset and clustering decisions and the sensitivity analysis described. The research question, ecological interpretation and conclusions remain with the research team.