bison {TwoStepCLogit}

Bison Dataset

Description

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

Format

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

Details

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).

References

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.

Examples

# 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).