Dummy Regression

[Maitane Roderiques]

Inregression analysis, a dummy variable (also known as indicator variable or just dummy) is one that takes a binary value (0 or 1) to indicate the absence or presence of some categorical effect that may be expected to shift the outcome.[1] For example, if we were studying the relationship between biological sex and income, we could use a dummy variable to represent the sex of each individual in the study. The variable could take on a value of 1 for males and 0 for females (or vice versa). In machine learning this is known as one-hot encoding.

Dummy variables are commonly used in regression analysis to represent categorical variables that have more than two levels, such as education level or occupation. In this case, multiple dummy variables would be created to represent each level of the variable, and only one dummy variable would take on a value of 1 for each observation. Dummy variables are useful because they allow us to include categorical variables in our analysis, which would otherwise be difficult to include due to their non-numeric nature. They can also help us to control for confounding factors and improve the validity of our results.

As with any addition of variables to a model, the addition of dummy variables will increase the within-sample model fit (coefficient of determination), but at a cost of fewer degrees of freedom and loss of generality of the model (out of sample model fit). Too many dummy variables result in a model that does not provide any general conclusions.

Dummy variables are useful in various cases. For example, in econometric time series analysis, dummy variables may be used to indicate the occurrence of wars, or major strikes. It could thus be thought of as a Boolean, i.e., a truth value represented as the numerical value 0 or 1 (as is sometimes done in computer programming).

Dummy variables may be extended to more complex cases. For example, seasonal effects may be captured by creating dummy variables for each of the seasons: D1=1 if the observation is for summer, and equals zero otherwise; D2=1 if and only if autumn, otherwise equals zero; D3=1 if and only if winter, otherwise equals zero; and D4=1 if and only if spring, otherwise equals zero. In the panel data fixed effects estimator dummies are created for each of the units in cross-sectional data (e.g. firms or countries) or periods in a pooled time-series. However in such regressions either the constant term has to be removed, or one of the dummies removed making this the base category against which the others are assessed, for the following reason:

If dummy variables for all categories were included, their sum would equal 1 for all observations, which is identical to and hence perfectly correlated with the vector-of-ones variable whose coefficient is the constant term; if the vector-of-ones variable were also present, this would result in perfect multicollinearity,[2] so that the matrix inversion in the estimation algorithm would be impossible. This is referred to as the dummy variable trap.

If I want a dummy for all levels of size except for a comparison group or base level, I do not need to create 4 dummies. Using [U] factor variables, I may type . summarize i.size or use an estimator

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I'm trying to create a series of dummy variables from a categorical variable using pandas in python. I've come across the get_dummies function, but whenever I try to call it I receive an error that the name is not defined.

For my case, dmatrices in patsy solved my problem. Actually, this function is designed for the generation of dependent and independent variables from a given DataFrame with an R-style formula string. But it can be used for the generation of dummy features from the categorical features. All you need to do would be drop the column 'Intercept' that is generated by dmatrices automatically regardless of your original DataFrame.

We want to perform linear regression of the police confidence score against sex, which is a binary categorical variable with two possible values (which we can see are 1= Male and 2= Female if we check the Values cell in the sex row in Variable View ). However, before we begin our linear regression, we need to recode the values of Male and Female. Why must we do this?

The codes 1 and 2 are assigned to each gender simply to represent which distinct place each category occupies in the variable sex . However, linear regression assumes that the numerical amounts in all independent, or explanatory, variables are meaningful data points. So, if we were to enter the variable sex into a linear regression model, the coded values of the two gender categories would be interpreted as the numerical values of each category. This would provide us with results that would not make sense, because for example, the sex Female does not have a value of 2.

A dummy variable is a variable created to assign numerical value to levels of categorical variables. Each dummy variable represents one category of the explanatory variable and is coded with 1 if the case falls in that category and with 0 if not. For example, in the dummy variable for Female, all cases in which the respondent is female are coded as 1 and all other cases, in which the respondent is Male, are coded as 0. This allows us to enter in the sex values as numerical. (Remember, these numbers are just indicators.)

Our sample of data has shown us that, on average, female respondents reported a police confidence score that is .436 points lower than male respondents. We want to know if this is a statistically significant effect in the population from which the sample was taken. To do this, we carry out a hypothesis test to determine whether or not b (the coefficient for females) is different from zero in the population. If the coefficient could be zero, then there is no statistically significant difference between males and females.

SPSS calculates a t statistic and a corresponding p-value for each of the coefficients in the model. These can be seen in the Coefficients output table. A t statistic is a measure of how likely it is that the coefficient is not equal to zero. It is calculated by dividing the coefficient by the standard error . If the standard error is small relative to the coefficient (making the t statistic relatively large), the coefficient is likely to differ from zero in the population.

The p-value is in the column labelled Sig . As in all hypothesis tests, if the p-value is less than 0.05, then the variable is significant at the 5% level. That is, we would have evidence to reject the null and conclude that b is different from zero.

In this example, t = -10.417 with a corresponding p-value of 0.000. This means that the chances of the difference between males and females that we have calculated is actually happening due to chance is very small indeed. Therefore, we have evidence to conclude that sex1 is a significant predictor of policeconf1 in the population.

For example, let's say a Field Category has the unique values of x,y and z. I want to create dummy_x, dummy_y and dummy_z with values of 1 or 0 based on the Category field. Now, I have more than 3 unique values and it is difficult to create the dummy variables one by one.

Am using the Feature Selection node in a linear regression model where the model includes dummy variables. I want to validate my understanding regarding the inclusion/exclusion of dummies with p-values indicating insignificance.

I believe that regardless of whether a specific dummy is significant or not, if one dummy is significant then they must all be included i.e. the (k-1) dummies actually included in the model as well as the reference dummy.

The KNIME Feature Selection Filter node will actually identify models where only one of the dummy variables is included in a referenced model. I believe this is misleading. How should I interpret the output of the Feature Selection Filter node in this case. Thanks in advance for any guidance!

This topic provides an introduction to dummy variables, describes how the software creates them for classification and regression problems, and shows how you can create dummy variables by using the dummyvar function.

The software chooses one of four schemes to define dummy variables based on the type of analysis, as described in the next sections. For example, suppose you have a categorical variable with three categories: Cool, Cooler, and Coolest.

X0 is a dummy variable that has the value 1 for Cool, and 0 otherwise. X1 is a dummy variable that has the value 1 for Cooler, and 0 otherwise. X2 is a dummy variable that has the value 1 for Coolest, and 0 otherwise.

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