2.3. Analytical Modeling

Probabilities of puppy training attendance were calculated for each year of age and the resulting data were fit with a single linear regression model to assess the relationship between dog age in years and the likelihood of attendance. Outlying points with high leverage, as indicated by a large Cook’s distance, were excluded from the regression. The confidence interval (CI) was calculated using the profile likelihood function without assumption of normality. The significance level was set to α ≤ 0.05 for all regression models in this manuscript.

Binary logistic regression models were built to assess the relationship between attending pre-adolescent training (true/false) and the occurrence of a specific behavior problem (true/false) when the effects of confounding or intervening background variables were accounted for. Separate models were constructed for each of the aforementioned behavior problems (i.e., 12 models were built). Background variables consisted of (1) whether or not the dog had been acquired at 12 weeks old or younger (true/false) as well as (2) dog sex (male/female), (3) neuter status (true/false), and (4) age at the time of the study. In all cases, the null hypothesis represented the statistically independent outcome. Odds ratios (ORs) were calculated as a measure of effect size. Confidence intervals were calculated using the profile likelihood function without assumption of normality. Multicollinearity was assessed using the variance inflation factor (VIF).

Additional binary logistic regression models were built to determine the relationship between variable factors of puppy training for those who had attended and the occurrence of a specific behavior problem (true/false) when the effects of confounding or intervening background variables were accounted for. The variable factors of puppy training we investigated consisted of (1) the starting age of attendance (≤3, 4, or 5–6 months), (2) number of classes attended (1–3, 4–6, 7–9, or 10+ classes), (3) type of training employed (reward-based/punishment-based), and (4) the use of restraining devices (one or more of: buckle collars, metal choke collar, prong, shock, nylon slip collar, harness, head halter, or martingale). The set of controlled background variables matched those mentioned previously and, similarly, separate models were built for each of the behavior problems (i.e., an additional 12 models were built). Effect size, confidence intervals, and multicollinearity were calculated and reported just the same. Per the default behavior of the generalized linear models produced by R’s stats package, entries with missing values for independent variables (e.g., no provided training starting age or number of attended classes) were automatically excluded from the models.