Categorical Variables in Regression
Categorical variables represent a qualitative method of scoring data (i.e. represents categories or group membership). These can be included in a regression analysis and treated as independent variables, but must be converted quantitatively in order to be able to analyze the data. One does so through the use of coding systems. Analyses are conducted such that only g -1 (g pertains to number of groups) are coded. This minimizes redundancy while still represents the complete data set as no additional information would be gained from coding the total g groups: for example, when coding gender (where g = 2: male and female), if we only code females everyone left over would necessarily be males. In general, the group you do not get data for is the group you are least interested in.
There are three main coding systems typically used in the analysis of categorical variables in regression: dummy coding, effects coding, and contrast coding. The regression equation takes the form of Y = bX + a, where b is the slope and gives you the weight of predicting a criterion, X is the explanatory variable, and a is the Y-intercept, and these values take on different meanings based on the coding system used. The choice of coding system does not affect the F or R² statistics. However, one chooses a coding system based on the comparison of interest since the interpretation of b values will vary.
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Famous quotes containing the words categorical and/or variables:
“We do the same thing to parents that we do to children. We insist that they are some kind of categorical abstraction because they produced a child. They were people before that, and they’re still people in all other areas of their lives. But when it comes to the state of parenthood they are abruptly heir to a whole collection of virtues and feelings that are assigned to them with a fine arbitrary disregard for individuality.”
—Leontine Young (20th century)
“The variables are surprisingly few.... One can whip or be whipped; one can eat excrement or quaff urine; mouth and private part can be meet in this or that commerce. After which there is the gray of morning and the sour knowledge that things have remained fairly generally the same since man first met goat and woman.”
—George Steiner (b. 1929)