Binary Logistic Regression#
Binary logistic regression is used to predict situations where the dependent variable is binary, meaning it has only two possible categories, such as 0 and 1, success and failure, yes and no, and so on. The basic idea of this model is to estimate the probability of a certain category based on a linear combination of independent variables. It usually uses the sigmoid function, also called the logistic function, to map predicted values between 0 and 1, thereby obtaining the probability that the event occurs.
- Dependent variable: binary variable, such as 0/1 or yes/no.
- Independent variables: can be quantitative continuous variables or qualitative categorical variables.
This model is widely used in healthcare, finance, marketing, and other fields. It is especially suitable for situations where you need to determine whether an event occurs, such as whether a customer purchases or whether a disease occurs.
Multinomial Logistic Regression#
Multinomial logistic regression handles cases where the dependent variable has multiple categories, meaning it contains three or more categories and those categories have no natural order. For example, predicting whether a person’s favorite color is red, blue, or green, or whether a person’s chosen transportation mode is bus, bicycle, or walking. Multinomial logistic regression extends multiple binary logistic regression models to multi-class cases, enabling classification among several categories.
- Dependent variable: multi-category variable, such as red, blue, green, and other categories.
- Independent variables: can be quantitative continuous variables or qualitative categorical variables.
This model is suitable when there is no order among categories, and it is commonly used in market research, consumer behavior analysis, and other fields.
Ordered Logistic Regression#
Ordered logistic regression handles cases where the dependent variable consists of ordered categories, meaning the dependent variable contains multiple categories with a natural order. For example, predicting a person’s satisfaction rating for a product may involve levels such as very dissatisfied, dissatisfied, neutral, satisfied, and very satisfied. This model assumes an order relationship among categories and uses a cumulative probability model to predict the dependent-variable category.
- Dependent variable: ordinal categorical variable, such as ordered categories 1, 2, 3, 4, and so on; for example, a satisfaction scale.
- Independent variables: can be quantitative continuous variables or qualitative categorical variables.
This model is widely used in market surveys, consumer satisfaction research, and other fields. It is especially suitable for scenarios where questions require rating by levels.
Supplement:#
In practical applications, scales are often used to represent ordinal categorical variables, especially in ordered logistic regression. For example, the Likert scale is a very typical ordinal scale. It usually includes five levels, such as strongly disagree, disagree, neutral, agree, and strongly agree. These levels have a clear order and are usually considered ordinal categorical variables.
