In multiple linear regression analysis, the measurement scale of the dependent variable is typically parametric. However, can multiple linear regression analysis be applied to a dependent variable measured on a nominal (non-parametric) scale?

This is a question that frequently arises and is often asked of me, especially when the variables in research are measured using categorical data. Multiple linear regression is generally used to predict the dependent variable based on independent variables, but this method may not always be suitable for non-parametric dependent variables.

I wrote this article to answer whether multiple linear regression analysis can be performed using a dependent variable measured on a nominal scale. Kanda Data will discuss this question in depth in this article.

**Definition of Nominal Scale Variables and Examples**

Before understanding the definition of nominal scale variables, we need to recall that measurement scales in statistics can be divided into four types: nominal, ordinal, interval, and ratio scales.

Nominal and ordinal measurement scales are known as non-parametric measurement scales, while interval and ratio scales are known as parametric measurement scales.

Variables measured using a nominal scale classify data into categories that have no meaningful order or numerical value. Data categories are created solely to differentiate between categories without any order or ranking.

Examples of variables measured using a nominal scale include gender (male/female), marital status (single/married), and favorite color (red/green/blue). From these examples, we can see that there is no ranking or hierarchy in these categories; they simply represent different groups.

**In Multiple Linear Regression, the Dependent Variable Typically Uses Ratio/Interval Variables**

In multiple linear regression, the dependent variable is usually measured using a ratio or interval scale, which has numerical properties with consistent intervals between values and a meaningful zero point (absolute zero). The use of parametric variables allows for a greater likelihood of meeting the assumptions required in multiple linear regression analysis using the least squares method.

Income, weight, or temperature variables are commonly used as dependent variables in linear regression analysis. In multiple linear regression, there are several assumptions that must be met, including normally distributed residuals, no multicollinearity, no heteroscedasticity, and other prerequisite assumptions to obtain the Best Linear Unbiased Estimator.

**How to Perform Regression Analysis for Nominal Scale Dependent Variables**

So, what if the dependent variable is non-parametric and measured using a nominal scale? When the dependent variable is nominal, multiple linear regression is no longer appropriate.

Instead, we can consider using logistic regression. Logistic regression is a statistical method that allows researchers to predict the outcome of a nominal dependent variable based on one or more independent variables. There are two types of logistic regression: binary (for dependent variables with two categories) and multinomial (for dependent variables with more than two categories).

When choosing to use logistic regression analysis, it is important to pay attention to its basic assumptions. These assumptions include: the relationship between independent variables and the log-odds of the dependent variable is linear, and there is no significant multicollinearity between the independent variables.

**Conclusion**

In data analysis with non-parametric dependent variables, such as those measured using a nominal scale, multiple linear regression is not the appropriate method. Instead, logistic regression is a more suitable approach, allowing researchers to effectively model the relationship between independent variables and nominal dependent variables.

By understanding the differences and appropriate applications of each method, researchers can conduct more accurate analyses and obtain more meaningful results from their data. That concludes the article that Kanda Data can share on this occasion. We hope it is useful to all of you. Stay tuned for updates on future articles from Kanda Data.