What is a Regression?

• A regression is a statistical method in which there are several independent variables (explanatory variables) that can be related to a dependent variable.
• It is possible to use regression models to determine whether changes observed in one or more explanatory variables are related to changes in the dependent variable.
• For the process, the data is dispersed around a best-fit line, which is fitted to the data.
• From asset valuation to making predictions, regression is useful to economists and financial analysts.
• Several assumptions must be made about the model and the data in order for regression results to be properly interpreted.

There are mainly three types of regression:

• Linear regression
• Non-linear regression
• Logistic regression

Regression is a vast topic and we all have a little less knowledge about it. Once you explore the regression you will get to know its capabilities to deal with different types of variables. Logistic regression lets you deal with multi-level dependent variables.

What is Ordinal Logistic Regression?

Ordinal logistic regression is actually a generalisation of multiple linear regression. It is used to find interactions between independent variables so that dependent variables can be predicted. This type of regression is used to predict the dependent variable with ‘ordered’ multiple categories and independent variables. Thus it facilitates the interaction of dependent with one or more independent variables. It predicts an ordinal dependent variable given one or more independent variables. Ordinal regression is also being used to determine the interactions between independent variables to predict the dependent variable. For example, a survey is done, in which there was a question on which the response lies between agreeing and disagree. This data doesn’t help in generalising well. Hence the level of responses further gets added as Strongly Disagree, Disagree, Agree, Strongly Agree. This offers a clear picture and is more realistic.

Assumptions

While using the ordinal regression to analyse your data, just make sure that your data "passes" the four assumptions mentioned below to give you a valid result. Also, make sure the test is conducted in this order only as any breach and you will no longer be able to use ordinal regression.

1. The dependent variable is measured on an ordinal level.
2. The independent variables are either continuous, categorical or ordinal. Examples of continuous variables include age (measured in years), revision time (measured in hours), income (measured in US dollars), intelligence (measured using IQ score), exam performance (measured from 0 to 100), weight (measured in kg) etc. Examples of categorical variables include gender (e.g., 2 groups: male and female), ethnicity (e.g., 3 groups: Caucasian, African American and Hispanic), profession (e.g., 5 groups: surgeon, doctor, nurse, dentist, therapist), and so forth.
3. No Multi-collinearity
4. It is an important step to check while calculating an ordinal regression. Also, this test includes creating dummy variables for your categorical variables as the number of dummy variables you have to create in SPSS Statistics depends on the number of categorical variables required to create.
5. Proportional Odds - each independent variable has an identical effect at each cumulative split of the ordinal dependent variable. This test in SPSS statistics is done using a full likelihood ratio test comparing the fitted location model to a model with varying location parameters.

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