interaction variable

(noun)

A variable constructed from an original set of variables to try to represent either all of the interaction present or some part of it.

Examples of interaction variable in the following topics:

  • Interaction Models

    • In regression analysis, an interaction may arise when considering the relationship among three or more variables.
    • If two variables of interest interact, the relationship between each of the interacting variables and a third "dependent variable" depends on the value of the other interacting variable.
    • The notion of "interaction" is closely related to that of "moderation" that is common in social and health science research: the interaction between an explanatory variable and an environmental variable suggests that the effect of the explanatory variable has been moderated or modified by the environmental variable.
    • An interaction variable is a variable constructed from an original set of variables in order to represent either all of the interaction present or some part of it.
    • When there are more than two explanatory variables, several interaction variables are constructed, with pairwise-products representing pairwise-interactions and higher order products representing higher order interactions.

  • Two-Way ANOVA

    • Two-way ANOVA examines the influence of different categorical independent variables on one dependent variable.
    • The two-way analysis of variance (ANOVA) test is an extension of the one-way ANOVA test that examines the influence of different categorical independent variables on one dependent variable.
    • Caution is advised when encountering interactions.
    • One should test interaction terms first and expand the analysis beyond ANOVA if interactions are found.
    • In this graph, the binary factor $A$ and the quantitative variable $X$ interact (are non-additive) when analyzed with respect to the outcome variable $Y$.

  • Multi-Factor Between-Subjects Designs

    • Moreover, there is a much bigger advantage than efficiency for including two variables in the same study: it allows a test of the interaction between the variables.
    • There is an interaction when the effect of one variable differs depending on the level of a second variable.
    • Recall that there is an interaction when the effect of one variable differs depending on the level of another variable.
    • The df for an interaction is the product of the df's of variables in the interaction.
    • A three-way interaction means that the two-way interactions differ as a function of the level of the third variable.

  • Exercises

    • Of the variables "gender" and "trials," which is likely to be a between-subjects variable and which a within-subjects variable?
    • Give an example of the "third-variable problem" other than those in this text.

  • Qualitative Variable Models

    • Dummy, or qualitative variables, often act as independent variables in regression and affect the results of the dependent variables.
    • Dummy variables are "proxy" variables, or numeric stand-ins for qualitative facts in a regression model.
    • In regression analysis, the dependent variables may be influenced not only by quantitative variables (income, output, prices, etc.), but also by qualitative variables (gender, religion, geographic region, etc.).
    • Qualitative regressors, or dummies, can have interaction effects between each other, and these interactions can be depicted in the regression model.
    • For example, in a regression involving determination of wages, if two qualitative variables are considered, namely, gender and marital status, there could be an interaction between marital status and gender.

  • Within-Subjects ANOVA

    • The degree to which the effect of dosage differs depending on the subject is the Subjects x Dosage interaction.
    • Recall that an interaction occurs when the effect of one variable differs depending on the level of another variable.
    • Since the error is the Subjects x Dosage interaction, the df for error is the df for "Subjects" (23) times the df for Dosage (3) and is equal to 69.
    • First, notice that there are two error terms: one for the between-subjects variable Gender and one for both the within-subjects variable Task and the interaction of the between-subjects variable and the within-subjects variable.
    • The degrees of freedom for the interaction is the product of the degrees of freedom for the two variables.

  • Glossary

    • Two independent variables interact if the effect of one of the variables differs depending on the level of the other variable.
    • An interaction plot displays the levels of one variable on the X axis and has a separate line for the means of each level of the other variable.
    • A linear combination of variables is a way of creating a new variable by combining other variables.
    • A predictor variable is a variable used in regression to predict another variable.
    • In analysis of variance, it is the sum of squared deviations from cell means for between-subjects factors and the Subjects x Treatment interaction for within subjects factors.

  • Models with Both Quantitative and Qualitative Variables

    • They are the statistic control for the effects of quantitative explanatory variables (also called covariates or control variables).
    • The regression relationship between the dependent variable and concomitant variables must be linear.
    • To see if the CV significantly interacts with the IV, run an ANCOVA model including both the IV and the CVxIV interaction term.
    • If the CVxIV interaction is significant, ANCOVA should not be performed.
    • If the CVxIV interaction is not significant, rerun the ANCOVA without the CVxIV interaction term.

  • Confounding

    • A confounding variable is an extraneous variable in a statistical model that correlates with both the dependent variable and the independent variable.
    • A confounding variable is an extraneous variable in a statistical model that correlates (positively or negatively) with both the dependent variable and the independent variable.
    • A perceived relationship between an independent variable and a dependent variable that has been misestimated due to the failure to account for a confounding factor is termed a spurious relationship, and the presence of misestimation for this reason is termed omitted-variable bias.
    • These two variables have a positive correlation with each other.
    • Controlling for known prognostic factors may reduce this problem, but it is always possible that a forgotten or unknown factor was not included or that factors interact complexly.

  • Exercises

    • An experimenter is interested in the effects of two independent variables on self-esteem.
    • What is better about conducting a factorial experiment than conducting two separate experiments, one for each independent variable?
    • Which statistical term (main effect, simple effect, interaction, specific comparison) applies to each of the descriptions of effects.
    • Plot an interaction for an A(2) x B(2) design in which the effect of B is greater at A1 than it is at A2.
    • The dependent variable is "Number correct. " Make sure to label both axes.