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Bison data collected in Prince Albert National Park, Saskatchewan, Canada (Craiu et al. 2011).

A data frame with 16818 observations on the following 10 variables.

- Cluster
pair of animals (dyad) ID

- Strata
stratum ID

- Y
response variable: 1 for visited locations, 0 otherwise

- water
land cover indicator covariate: 1 for water, 0 otherwise

- agric
land cover indicator covariate: 1 for agricultural locations , 0 otherwise

- forest
land cover indicator covariate: 1 for forests, 0 otherwise

- meadow
land cover indicator covariate: 1 for meadows, 0 otherwise

- biomass
continuous covariate: above-ground vegetation biomass index measured (in

*kg/m^2*) only at locations within meadows, 0 otherwise- pmeadow
continuous covariate: the proportion of meadow in a circular plot (700 m in radius) centered at the bison's location

This data set was collected in order to study habitat selection by groups of free-ranging bison. For each observed group, two individuals (dyad) equipped with GPS radio-collars were followed simultaneously. A cluster is defined here as a pair of bison. This data set contains 20 clusters. The number of strata per cluster varies between 13 and 345 for a total of 1410 strata. A stratum is composed of two visited GPS locations (one for each individual) gathered at the same time, together with 10 random locations (five drawn within 700 m of each of the two focal bison). Therefore, there are 12 observations per stratum, with 2 cases (Y=1) and 10 controls (Y=0). However, due to problems in the data collection, 17 of the 1410 strata have only 6 observations (1 case and 5 controls).

Craiu, R.V., Duchesne, T., Fortin, D. and Baillargeon, S.
(2011), Conditional Logistic Regression with Longitudinal Follow-up and
Individual-Level Random Coefficients: A Stable and Efficient Two-Step
Estimation Method, *Journal of Computational and Graphical Statistics*. **20**(3), 767-784.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 | ```
# Some descriptive statistics about the data set:
ddim(formula = Y ~ strata(Strata) + cluster(Cluster), data = bison)
# Model 1: covariates meadow, biomass and biomass^2
# Random effects in front of biomass and biomass^2
# Main diagonal covariance structure for D
Fit1 <- Ts.estim(formula = Y ~ meadow + biomass + I(biomass^2) +
strata(Strata) + cluster(Cluster), data = bison,
random = ~ biomass + I(biomass^2), all.m.1=FALSE, D="UN(1)")
Fit1
# Model 2: only covariates biomass and biomass^2
# Random effects in front of biomass and biomass^2
# Main diagonal covariance structure for D
Fit2 <- Ts.estim(formula = Y ~ biomass + I(biomass^2) + strata(Strata) +
cluster(Cluster), data = bison, all.m.1=FALSE, D="UN(1)")
Fit2
# Results reported in Table 2 of Craiu et al. (2011).
``` |

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