Overall, the discriminant analysis and the multiple regression are similar in that they both construct a weighted linear combination of scores on several independent variables (Warner 2013). This combination ought to be optimal, meaning that it should predict the scores on the outcome variable from the scores on the predictor variables in the most precise manner (Warner, 2013).
On the other hand, the discriminant analysis and the multiple regression differ in the following. The multiple regression utilizes a continuous variable as an outcome (although a binary logistic regression uses dichotomous outcome variables; Warner, 2013). The discriminant analysis deals with an outcome that is expressed as a categorical variable (George & Mallery, 2016). Also, there exists a specific conceptual difference: in a regression, the outcome is predicted from the independent variables, whereas in the discriminant analysis, an attempt is made to predict the values of the independent variables based on the values of the dependent variable (Field, 2013).
As for the choice of the type of analysis, the discriminant analysis and the multiple regression may both be utilized in various situations. However, multiple regression can sometimes be preferred to the discriminant analysis because it requires less restrictive assumptions to be met to be valid (Warner, 2013). Furthermore, the logistic regression may be chosen over the discriminant analysis when needed to estimate the probability of a particular outcome given a change in scores on predictor variables. The discriminant analysis is more capable of supplying information useful for distinguishing between various groups, describing the dimensions on which these groups differ from one another (Warner, 2013). Thus, the criteria for choosing one analysis over the other depending on the desired outcome of the analysis and the capability of the data to meet the needed assumptions.
References
Field, A. (2013). Discovering statistics using IBM SPSS Statistics (4th ed.). Thousand Oaks, CA: SAGE Publications.
George, D., & Mallery, P. (2016). IBM SPSS Statistics 23 step by step: A simple guide and reference (14th ed.). New York, NY: Routledge.
Warner, R. M. (2013). Applied statistics: From bivariate through multivariate techniques (2nd ed.). Thousand Oaks, CA: SAGE Publications.