Researchers have begun studying the impact of human opioid and cannabinoid use on dog populations. These studies have used data from an animal poison control center (APCC) and there are concerns that due to the illicit nature and social stigma concerning the use of these drugs, owners may not always be forthcoming with veterinarians or APCC staff regarding pet exposures to these toxicants. As a result, models derived from APCC data that examine the predictability of opioid and cannabinoid dog poisonings using pet demographic and health disorder information may help veterinarians or APCC staff more reliably identify these toxicants when examining or responding to a call concerning a dog poisoned by an unknown toxicant. The fitting of epidemiologically informed statistical models has been useful for identifying factors associated with various health conditions and as predictive tools. However, machine learning, including lasso regression, has many useful features as predictive tools, including the ability to incorporate large numbers of independent variables. Consequently, the objectives of our study were: 1) identify pet demographic and health disorders associated with opioid and cannabinoid dog poisonings using ordinary and mixed logistic regression models; and 2) compare the predictive performance of these models to analogous lasso logistic regression models. Data were obtained from reports of dog poisoning events collected by the American Society for the Prevention of Cruelty to Animals’ (ASPCA) Animal Poisoning Control Center, from 2005–2014. We used ordinary and mixed logistic regression models as well as lasso logistic regression models with and without controlling for autocorrelation at the state level to train our models on half the dataset and test their predictive performance on the remainder. Although epidemiologically informed logistic regression models may require substantial knowledge of the disease systems being investigated, they had the same predictive abilities as lasso logistic regression models. All models had relatively high predictive parameters except for positive predictive values, due to the rare nature of calls concerning opioid and cannabinoid poisonings. Ordinary and mixed logistic regression models were also substantially more parsimonious than their lasso equivalents while still allowing for the epidemiological interpretation of model coefficients. Controlling for autocorrelation had little effect on the predictive performance of all models, but it did reduce the number of variables included in lasso models. Several disorder variables were associated with opioid and cannabinoid calls that were consistent with the acute effects of these toxicants. These models may help build diagnostic evidence concerning dog exposure to opioids and cannabinoids, saving time and resources when investigating these cases.