Theobald et al. (2019) explore the appropriateness of various types of regression models. Despite the importance of regression in testing hypotheses, the authors were concerned that linear regression is used without regard to appropriateness. Linear regression analysis assumes linearity, equal variance of errors, independence of errors, and normality of errors. Often, researchers get into the trap of using linear regression in breach of the assumptions leading to inaccurate results and interpretations. While linear regression is effective for continuous variables, it is inappropriate when modeling binary, count, or categorical variables. Theobald et al. (2019) evaluate the use of generalized regression models in place of linear regression where necessary. The generalized models considered include Poisson, logistic, binomial, proportions odd logistic, and multinomial regression models.
Theobald et al. (2019) suggest situations where each of the generalized models is appropriate. The logistic regression model is suitable when studying categorical data with two possible outcomes, such as failing or passing exams. The two possible outcomes in logistic regression are represented as 0 or 1 and result in a nonlinear relationship against the assumptions in linear regression. The binomial regression model is used if the results are proportions estimated by calculating the number of successes and failures in several trials. The data results in nonlinear relationships, for example, when studying the proportion of mathematics students who graduate from an institution. Proportional odd logistics regression provides a way of analyzing categorical, ordinal data such as a variable that measures customer satisfaction on a Likert scale of 1 to 10. Multinomial regression models are used if two categorical variables cannot be ranked because one level is not necessarily better or more significant than the other, for example, when jointly evaluating the graduating proportions of students from an institution and the proportions of dropouts who join other institutions and still graduate. The Poisson regression model uses count data which, unlike in the binomial regression model, is unbound. An example is when modeling the number of times instructors record an event as compared to students.
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When using a linear regression model, the data set must be normally distributed, meaning that the statistics are appropriate estimates of the population parameters. When a data set is normally distributed, the central tendency measures of a sample are an estimation of the central tendencies of the population. However, the generalized regression models do not assume normality of data meaning that the data may have a skewed distribution, in which case the sample statistics would not be proper estimates of the population parameters. Contrary to the slope in a linear regression model, generalized models involve calculating odds ratios ( Theobald et al., 2019). For example, the odds in a logistic regression model are calculated using the formula . For example, if the odds in a logistic regression model are = 2.04 means that a unit change in the independent variable for participants reporting negative,0 outcome causes as twice as much of the participant to report positive outcome, 1.
Theobald et al. (2019) discuss numerous violations that may occur when using regression. The findings provide essential information that can be used to improve the accuracy of hypothesis testing conducted using regression. The objectives of the article are achieved through the broad literature on the appropriateness of the generalized regression models and numerous examples on suitability and interpretation of outcomes. Theobald et al. (2019) is a helpful guide for researchers seeking to find the appropriate regression model to analyze a set of data. Besides providing helpful information, the article is adequately cited and points readers to other valuable sources for more information on the topic.
Reference
Theobald, E. J., Aikens, M., Eddy, S., & Jordt, H. (2019). Beyond linear regression: A reference for analyzing common data types in discipline based education research. Physical Review Physics Education Research, 15(2), 020110.
