The analysis of Ordinary Least Squares (OLS) linear regression is most commonly used to estimate the influence of independent variables on a dependent variable. In OLS linear regression analysis, several assumptions must be fulfilled to obtain the best linear unbiased estimator.
If you often read research papers accessed through Google Scholar, you may come across OLS linear regression and logistic regression. What are the main differences between these two types of regression? Furthermore, what assumptions are required?
Considering the significance of understanding both types of regression for researchers, in this article, Kanda Data will discuss the differences between logistic regression and OLS linear regression.
Key Differences Between OLS Linear Regression and Logistic Regression
To select the appropriate regression test, researchers need to understand the distinctions between when to use OLS linear regression and when to employ logistic regression. Researchers commonly employ OLS linear regression to observe the influence of independent variables on a dependent variable. This OLS linear regression method can be applied to cross-sectional and time-series data.
Researchers need to conduct several assumption tests to achieve unbiased and consistent estimation results. These assumption tests include tests for residual normality, non-heteroskedasticity, linearity, and non-multicollinearity, and additional tests for autocorrelation specifically designed for time-series data.
Based on the experience from several previous studies, the measurement scale of data will determine the fulfillment of these assumption tests.
Moving on to logistic regression testing, it differs from OLS linear regression. Researchers often use logistic regression when the influencing variable (dependent variable) is non-parametric.
A dependent variable measured on a nominal scale can consider using logistic regression. When the dependent variable on a nominal scale has two categories, it is called binary logistic regression.
Conversely, in OLS linear regression, the dependent variable is typically parametric. Parametric variables can be measured using either a ratio or interval scale. Thus, we can conclude that the measurement scale of the variable will dictate the appropriate choice of regression test.
Differences in Measurement Scales: Nominal, Ordinal, Interval, and Ratio
The measurement scale of variables plays a crucial role in data analysis. Based on their measurement scales, variable data can be categorized into four types: nominal scale, ordinal scale, interval scale, and ratio scale.
For variables measured on a nominal or ordinal scale, consideration can be given to using non-parametric statistics. On the other hand, parametric statistics may be more appropriate for variables measured on an interval or ratio scale.
The nominal scale involves categorizing variables without any inherent order or ranking. Its categorization merely distinguishes between different categories. Examples of the nominal scale include gender and occupation.
For example, gender is divided into male and female. The categorization of males and females lacks a hierarchical order – there is no assumption that one is higher or lower than the other. Similarly, in the case of occupation, there is no assumption that one job is superior to another.
The second measurement scale is the ordinal scale. Categorization in the ordinal scale is similar to the nominal scale but with the distinction that the ordinal scale includes a sense of hierarchy or ranking.
A simple example is educational attainment. Within educational levels, it can be determined that someone with a college degree has a higher education level than someone with a high school diploma. Similarly, someone with a junior high school education ranks higher in education than someone with an elementary school education.
Moving on to the third scale, the interval scale. In the interval scale, numerical values are present in the data but do not possess an absolute zero point. Examples of this scale include temperature and test scores.
Lastly, the ratio scale involves numerical data with an absolute zero point. Examples include profit, cost, quantity of seeds, amount of fertilizer, and so on.
Determining the Need for Logistic Regression
Once we understand the differences between measurement scales – nominal, ordinal, interval, and ratio – we can make an informed choice regarding the appropriate statistical analysis.
The easiest way to identify the need for logistic regression is by considering the measurement scale of the dependent variable. If the dependent variable is measured on a nominal scale with two categories, then binary logistic regression analysis may be worth considering.
However, if the dependent variable is measured on an interval or ratio scale, then linear regression using the OLS method could be a suitable option. Nevertheless, researchers should also be aware that both regression methods have certain assumptions that must be met.
Ensure that a series of assumption tests have been conducted to attain consistent and unbiased estimation results. Ensuring that the interpretation and conclusions drawn from the research outcomes are accurate, and error-free is essential.
Understand the Basic Theory of the Chosen Analysis
After researchers grasp the distinctions between utilizing logistic regression and OLS linear regression, the next step is comprehending the fundamental theory. This basic theory can be divided into two parts: the foundational theory of the researched topic and the foundational theory of using statistical analysis tools.
Researchers should refer to theory when constructing the specification of regression equations, whether for logistic regression or OLS linear regression.
Subsequently, researchers can build upon existing theories. They can confirm previous research findings or even embark on entirely new research that has not been conducted before.
Furthermore, the theory that researchers need to comprehend encompasses the theory of employing statistical tests. For instance, researchers must understand the theory behind the application of logistic regression and also the theory behind using OLS linear regression.
Conduct Data Analysis and Interpretation Exercises
It is recommended that researchers engage in data analysis exercises and interpretation methods to enhance theirs. Data analysis exercises should not only encompass the main analyses but also include the required assumption tests.
Researchers can also read previous research findings on how to interpret and draw conclusions from both logistic regression and OLS linear regression analyses.
As a result, once researchers have grasped the foundational theory and have practiced data analysis and interpretation, it is expected to facilitate the completion of their research.
Based on the preceding paragraphs, it can be concluded that when researchers choose data analysis tools, they need to comprehend the differences in measurement scales: nominal, ordinal, interval, and ratio.
The easiest way to detect the need for logistic regression and OLS linear regression is by considering the measurement scale of the dependent variable. If the dependent variable is measured on a nominal scale with two categories, then binary logistic regression can be considered.
Subsequently, researchers need to ensure that the requisite assumption tests have been carried out and adhere to statistical principles, whether using logistic or OLS linear regression. It concludes the article that Kanda Data can present at this time. We hope it proves beneficial for everyone. Stay tuned for the next week’s educational article updates from Kanda Data!
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