![]() The variable wordsum is a measure of respondent literacy based on the number of correct responses on a vocabulary test. It can be considered as a measure of belief in government for these purposes. Items were tested for internal consistency and included all observations with at least one response. The variable govhelp was compiled following factor analysis of survey items and is based on four questions asking respondents the extent to which they believe government should be involved in helping certain groups. The variable has a range of 1–4 with a mean of 2.94 and can be considered as continuous for the purposes of this example. Likert-scale response options ranged from strongly agree to strongly disagree with a high score meaning strong disagreement. It is much better for everyone involved if the man is the achiever outside the home and the woman takes care of the home and family. It is possible to have three-way interactions or more, but we focus on the two-way case for ease of explanation. This example will focus on interactions between one pair of variables that are both continuous in nature. An interaction can occur between independent variables that are categorical or continuous and across multiple independent variables. In a linear regression model, the dependent variables should be continuous. Focus is given instead to the difference in slopes which is described by the interaction coefficient. ![]() In a model including an interaction term, the slope estimates cannot be interpreted in the same way as they are now conditional on other values. Most attention is focused on the slope estimates because they capture the relationship between the dependent and independent variables. This requires estimating an intercept (often called a constant) and a slope for each independent variable that describes the change in the dependent variable for a one-unit increase in the independent variable. ![]() In a “main effects” multiple regression model, a dependent (or response) variable is expressed as a linear function of two or more independent (or explanatory) variables. Interaction describes a particular type of non-linear relationship, where the “effect” of an independent variable on the dependent variable differs at different values of another independent variable in the model. ![]()
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