Logistic Regression with Dummy Variables as regressors?

The process of analyzing this type of problem involves considering the mode of dismissal (categorical response), time spent at the crease and balls faced (numerical regressors), and position down the order (categorical regressor). In summary, you can use a logistic regression approach with modified linear predictor to analyze a model with both dummy variable regressors and categorical response variables.
  • #1
maverick280857
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Hi

Is it possible to use both dummy variable regressors as well as categorical response variables in the same model? Consider the following model from cricket (you don't need to know the game to answer this question):

Y = mode of dismissal (0 = not out, 1 = bowled, 2 = caught, 3 = stumped, etc.) [categorical]
X1 = time spent at the crease [numerical]
X2 = balls faced [numerical]
X3 = position down the order (1 = opening, 2 = one-down, etc.) [categorical/dummy]

In this case can we use the logistic regression approach with the linear predictor modified to include one or more dummy variables?

The usual logistic regression setup consists of a categorical response and numerical regressors. I am asking if we can have 1 categorical response, 2 numerical regressors and 1 categorical regressor.

How does one analyze such a problem?

Thanks in advance.

Vivek
 
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  • #2
Yes, it is possible to use both dummy variable regressors as well as categorical response variables in the same model. You can analyze such a problem using a logistic regression approach with a linear predictor modified to include one or more dummy variables. This setup consists of the categorical response, two numerical regressors, and one categorical regressor.
 

1. What is logistic regression and how is it different from linear regression?

Logistic regression is a statistical method used to predict the probability of a binary outcome (such as yes/no or true/false) based on one or more independent variables. It differs from linear regression in that it models the relationship between the independent variables and the log odds of the outcome, rather than the outcome itself. This allows for non-linear relationships and more accurate predictions for binary outcomes.

2. What are dummy variables and why are they used as regressors in logistic regression?

Dummy variables are categorical variables that are coded as numerical values, typically 0 or 1. They are used in logistic regression to represent categories or groups of a categorical variable. This allows for the inclusion of categorical variables in the regression model, as logistic regression can only handle numerical inputs.

3. How do you interpret the coefficients of dummy variables in a logistic regression model?

The coefficients of dummy variables in a logistic regression model represent the difference in the log odds of the outcome between the reference category (the category with a coefficient of 0) and the dummy variable's category. For example, if the coefficient for a dummy variable representing gender is 0.5, it means that the log odds of the outcome for that gender is 0.5 higher than the log odds for the reference gender.

4. Can you use more than two dummy variables for a single categorical variable in logistic regression?

Yes, you can use multiple dummy variables for a single categorical variable in logistic regression. However, it is important to ensure that the dummy variables are not perfectly correlated with each other, as this can lead to issues with the model's interpretability and accuracy.

5. What are some common assumptions of logistic regression with dummy variables?

Some common assumptions of logistic regression with dummy variables include: 1) the relationship between the independent variables and the log odds of the outcome is linear, 2) there is no multicollinearity among the independent variables, 3) the error terms are independent, 4) the error terms are normally distributed, and 5) the error terms have equal variance. Violations of these assumptions can affect the accuracy and interpretation of the model results.

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