Ordinal Logistic Regression using SPSS

What is it All About?

Ordinal Logistic regression analysis is a method to determine the reason-result relationship of independent variable(s) with an Ordinal dependent variable

Learn to Analyze Data using Ordinal Logistic Regression using SPSS

The tutorial is a step by step guide on how to perform Ordinal Logistic Regression using SPSS.

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The Concept of Ordinal Logistic Regression

"What to do when we have a Likert Scale outcome variable in Research"

Regression technique is used to assess the strength of a relationship between one dependent and independent variable(s). It helps in predicting value of a dependent variable from one or more independent variable.

Linear regression analysis requires the outcome/criterion variable to be measured as a continuous variable. However, there may be situations when the researcher would like to predict an outcome that is Ordinal (for instance Strongly Disagree to Strongly Agree).

In such situation, a scholar can use Ordinal Logistic Regression to assess the impact of one of more predictor variables on the outcomes. Ordinal Logistic regression analysis is a method to determine the reason-result relationship of independent variable(s) with dependent variable

Examples of Ordinal Logistic Regression

A scholar may utilize Ordinal logistic regression in following situations

A restaurant would like to assess factors that lead to higher customer satisfaction ratings (Strongly Dis-satisfied (1) to Strongly Satisfied(5)).
A college would like to assess student confidence level (Low (1) to High (5)) of a student based on Age, Grade, Aptitude Test Results.
A HR researcher would like to ascertain how factors like experience, years of education, previous salary, university ranking affect the selection chances of a candidate in a job interview (Low (1) to High (5).
A scholar would like to predict interest of University Students in their studies (Low (1) to High (5)) based on independent variables that include Assignments, Co-curricular activities, Gender, and Age.

Assumptions

Logistic regression does not assume a linear relationship between the dependent and independent variables.
The independent variables need not be interval, nor normally distributed, nor linearly related, nor of equal variance within each group
Homoscedasticity is not required. The error terms (residuals) do not need to be normally distributed.
The dependent variable in logistic regression is not measured on an interval or ratio scale. The dependent variable must be a dichotomous ( 2 categories) for the binary logistic regression.
The categories (groups) as a dependent variable must be mutually exclusive and exhaustive; a case can only be in one group and every case must be a member of one of the groups.
Larger samples are needed than for linear regression because maximum coefficients using a ML method are large sample estimates. A minimum of 50 cases per predictor is recommended (Field, 2013)
Hosmer, Lemeshow, and Sturdivant (2013) suggest a minimum sample of 10 observations per independent variable in the model, but caution that 20 observations per variable should be sought if possible.
Leblanc and Fitzgerald (2000) suggest a minimum of 30 observations per independent variable.

Example Problem

For the purpose of this tutorial, i am considering the following example.

A scholar would like to predict interest of University Students in their studies (Low (1) to High (5)) based on independent variables that include Assignments, Co-curricular activities, Gender, and Age.

How to Run Ordinal Logistic Regression

Step 1: In SPSS, Go to Analyze -> Regression -> Ordinal

Step 2: Next, The Ordinal Logistic Regression Dialog Box will Appear. Add Interest in the Dependent Box and Add IVs, Assignments, CCA, and Gender in the Factor(s) List Box and Age in the Covariates list box.

Step 3: Next, Select Options, make sure Logit is selected from Link combo box.

Step 4: Press, Output, and Select Test of Parallel Lines.

Interpreting Ordinal Logistic Regression

Case Processing Summary and Encoding

The first section of the output shows Case Processing Summary highlighting the cases included in the analysis. In this example we have a total of 144 respondents.

Goodness-of-fit statistics help you to determine whether the model adequately describes the data.

Model Fitting Information, If the Model is significant, this shows that there is a significant improvement in fit as compared to the null model, hence, the model is showing a good fit.

The difference between Intercept Only Model and Final Model should be significant.

Next,

Goodness of Fit statistic indicates a poor fit if the significance value is less than 0.05. Here, the model adequately fits the data (p > 0.05).

A goodness-of-fit test, in general, refers to measuring how well do the observed data correspond to the fitted (assumed) model.

Here, an insignificant value would mean that there are no significant differences in the observed data and fitted (assumed) model.

Model Summary - Psuedo R Square

Model Summary shows the Psuedo R-Square. Psuedo means that it is not technically explaining the variation. But they can be used as approximate variation in the criterion variable. In Ordinal Regression we will use McFadden value of R-Square.

In this case we can say that there has been a 10.4 % improvement in the prediction of outcome based on the predictors in comparison to the null model.

Parameter Estimates

Estimate shows probability of a case falling above a given category on the dependent variable.
The Sign is interpreted as linear regression
+ sign is associated with an increase likelihood of case falling into a higher category in the dependent variable.
– sign is associated with an increase likelihood of case falling into a lower category in the dependent variable.
For instance, a Positive Sign with Age (0.315) would mean that with increasing Age there is a higher interest in studies.

As for Assignment, Students who receive an assignment have higher interest in studies in comparison to those who do not receive an assignment. However, the difference is insignificant.
As for the impact of Co-curricular activities (CCA), those students who have very little chance of participating in CCA, have lower interest in studies as compared to those who participate in CCA Quite Often.
In terms of Gender, Male students had a higher interest in studies in comparison to Female Students.

Odds Ratio

Odds Ratio Represents the Odds of Falling into a Higher/Lower Category on the Dependent Variable with a Unit Change in the Independent Variable.
OR>1 shows an increasing Odds of being in a higher category with a unit increase in the predictor.
OR<1 shows decreasing Odds of being in a higher category with a unit increase in the predictor.

The Odds of higher interest in studies are 1.370 times greater for higher aged students in comparison to low aged students
The odds for having interest in studies are 0.964377 times low when students do not receive an assignment.
The Odds of taking interest in studies increase with increasing co-curricular activities. This shows that the Odds of increasing interest in studies will decrease if there very few co-curricular activities.
The odds of Male Students having a higher Interest in studies is greater in comparison to Females by 3.391.

Test of Parallel Lines

Assumption of Ordinal Logistic Regression
Odds of Falling into the a higher (vs. Lower) category on the DV are the same across categories.
In Simple Terms, The effects of the predictors are the same across the levels of the dependent variable.
Odds of predictor falling into the categories on the DV are the same across the response categories.
P value is expected to be insignificant.
If P Value is significant, use Multinomial Logistic Regression.
A significant Test of Parallel lines would mean that probability of falling to a higher category does not vary across categories on the DV for the predictors.