Ordinal Logistic Regression in SPSS

Discover Ordinal Logistic Regression in SPSS! Learn how to perform, understand SPSS output, and report results in APA style. Check out this simple, easy-to-follow guide below for a quick read!

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Introduction

Welcome to an informative journey into the world of Ordinal Logistic Regression in SPSS. This advanced statistical technique holds a unique position in data analysis, allowing researchers to understand and predict outcomes that fall into ordered categories. In this blog post, we’ll explore the fundamental concepts behind ordinal logistic regression, its applications, and how to make the most of this versatile tool in SPSS.

Whether you’re a seasoned data analyst or a newcomer to the world of statistics, this guide will equip you with the knowledge and skills to effectively utilise ordinal logistic regression for your research needs.

Types of Logistic Regression

Before delving into binary logistic regression, let’s take a moment to explore the broader landscape of logistic regression. There are three primary types: Binomial Logistic Regression, Multinomial Logistic Regression, and Ordinal Logistic Regression.

  • Binomial Logistic Regression deals with binary outcomes, where the dependent variable has only two possible categories, such as yes/no or pass/fail.
  • Multinomial Logistic Regression comes into play when the dependent variable has more than two unordered categories, allowing us to predict which category a case is likely to fall into.
  • Ordinal Logistic Regression is employed when the dependent variable has multiple ordered categories, like low, medium, and high, enabling us to predict the likelihood of a case falling into or above a specific category.

In this post, our focus will be on Ordinal Logistic Regression, which is widely used for binary outcomes and forms the foundation for understanding logistic regression.

Definition: Ordinal Logistic Regression

Ordinal Logistic Regression is a powerful statistical method designed to handle dependent variables that are ordinal, meaning they have ordered categories. Unlike binary logistic regression which deals with binary outcomes, ordinal logistic regression caters to situations where the dependent variable falls into three or more ordered and distinct categories, but the intervals between these categories are not precisely defined. This makes it a valuable tool in various fields, including psychology, social sciences, and marketing, where researchers seek to understand and predict outcomes such as customer satisfaction levels, educational attainment, or job satisfaction.

Ordinal logistic regression extends the principles of binary logistic regression to ordered categories by modeling the cumulative probabilities of an observation falling into or below a particular category. By the end of this blog post, you’ll have a solid understanding of how to apply ordinal logistic regression to your data, interpret the results, and draw meaningful conclusions from your analysis.

Logistic Regression Equation

The ordinal logistic regression equation represents the mathematical relationship between the predictor variables and the log odds of an observation belonging to a specific ordinal category or a lower category. The equation takes the following form:

Log[P(Y ≤ j) / (1 – P(Y ≤ j))] = α_j + β_1X_1 + β_2X_2 + … + β_pX_p

In this equation:

  • P(Y ≤ j) represents the cumulative probability of the dependent variable ( Y ) being in category ( j) or lower.
  • (α_j) is the intercept term specific to category ( j ).
  • (β _1, β _2, ….., β _p) are the regression coefficients associated with each predictor variable ( X_1, X_2, …., X_p ).
  • ( X_1, X_2, …, X_p ) are the predictor variables used in the analysis.

The logistic regression equation models the log odds of an observation belonging to or below category ( j ) compared to the odds of it belonging to a higher category. These log odds are then transformed into probabilities.

To classify an observation into a specific category, you would compare the cumulative probabilities for each category and select the one with the highest probability. The coefficients (β) in the equation quantify the impact of each predictor variable on the log odds of category membership.

Assumptions of Ordinal Logistic Regression

Before applying ordinal logistic regression to your data, it’s crucial to consider the assumptions that underlie this statistical technique. These assumptions ensure the reliability and validity of your analysis. Here’s a list of the key assumptions of ordinal logistic regression:

  • Proportional Odds Assumption: This is the fundamental assumption of ordinal logistic regression. It posits that the relationship between the predictors and the odds of being in a higher versus lower category remains consistent across all categories. In other words, the effect of the predictors on the outcome should be consistent along the ordinal scale.
  • Independence of Observations: Like many statistical methods, ordinal logistic regression assumes that observations are independent of each other. This means that the outcome of one observation should not be influenced by the outcome of another. It’s essential to verify this assumption, especially in survey or experimental designs where independence might be compromised.
  • Linearity of Log-Odds: Ordinal logistic regression assumes that the relationship between the log-odds of being in a specific category and the predictor variables is linear. Non-linear relationships can affect the model’s accuracy, so it’s important to check this assumption.
  • No Perfect Multicollinearity: As in other regression techniques, ordinal logistic regression assumes that there is no perfect multicollinearity among the predictor variables. Perfect multicollinearity occurs when one predictor variable can be predicted perfectly from a combination of others, leading to unstable coefficient estimates.
  • Adequate Sample Size: To ensure the stability and validity of the results, a sufficient sample size is required. The specific requirements can vary depending on the complexity of the model and the number of predictor variables.

Adhering to these assumptions is essential when applying ordinal logistic regression to your data. Violations of these assumptions can lead to inaccurate results and misinterpretations, so it’s important to assess and address them appropriately.

Hypothesis of Ordinal Logistic Regression

In ordinal logistic regression, hypotheses play a critical role in the research process. They guide the analysis and interpretation of results, helping researchers draw meaningful conclusions. Here are the key hypotheses involved in ordinal logistic regression:

  • Null Hypothesis (H0): there is no significant relationship between the predictor variables and the odds of being in a particular category or lower on the ordinal scale.
  • Alternative Hypothesis (H1): there is a significant relationship between the predictor variables and the odds of being in a particular category or lower.

Hypothesis testing is a crucial step in ordinal logistic regression, as it helps determine whether the predictor variables have a meaningful impact on the ordinal outcome variable. By testing these hypotheses, researchers can assess the significance of predictor variables and make informed decisions about their inclusion in the model. The results of hypothesis testing provide valuable insights into the factors influencing category membership on the ordinal scale.

 An Example of Ordinal Logistic Regression

To illustrate Ordinal Logistic Regression in practice, let’s consider a study examining the factors influencing customer satisfaction levels. Firstly, the dependent variable, customer satisfaction, is ordinal with categories like ‘Unsatisfied’, ‘Neutral’, and ‘Satisfied’. Secondly, the independent variables could include factors like service quality, price, and location.

Using SPSS to perform Ordinal Logistic Regression, researchers can uncover the relationships between these factors and customer satisfaction. Firstly, the model would reveal which factors are significant predictors of satisfaction levels. Secondly, the odds ratios provide insights into how much each factor increases or decreases the odds of a customer being in a higher satisfaction category, offering valuable guidance for business strategies and customer service improvements.

 

How to Perform Ordinal Logistic Regression in SPSS

Step by Step: Running Ordinal Logistic Regression in SPSS Statistics

Now, let’s delve into the step-by-step process of conducting the Ordinal Logistic Regression using SPSS Statistics.  Here’s a step-by-step guide on how to perform an Ordinal Logistic Regression in SPSS:

  1. STEP: Load Data into SPSS

Commence by launching SPSS and loading your dataset, which should encompass the variables of interest – a categorical independent variable. If your data is not already in SPSS format, you can import it by navigating to File > Open > Data and selecting your data file.

  1. STEP: Access the Analyze Menu

In the top menu, locate and click on “Analyze.” Within the “Analyze” menu, navigate to “Regression” and choose ” LinearAnalyze > Regression> Ordinal

  1. STEP: Choose Variables

In the Ordinal Logistic Regression dialog box, move the ordinal outcome variable into the “Dependent” box and the categorical predictor variables into the “Factors (s)” box. And Dummy or continuous predictors into the “Covariance (s)” box.

Click “Output” and check “Goodness-of-fit” and “Parameter estimates”

  1. STEP: Generate SPSS Output

Once you have specified your variables and chosen options, click the “OK” button to perform the analysis. SPSS will generate a comprehensive output, including the requested frequency table and chart for your dataset.

Executing these steps initiates the Ordinal Logistic Regression in SPSS, allowing researchers to assess the impact of the teaching method on students’ test scores while considering the repeated measures. In the next section, we will delve into the interpretation of SPSS output for Ordinal Logistic Regression.

Note

Conducting an Ordinal Logistic Regression in SPSS provides a robust foundation for understanding the key features of your data. Always ensure that you consult the documentation corresponding to your SPSS version, as steps might slightly differ based on the software version in use. This guide is tailored for SPSS version 25, and for any variations, it’s recommended to refer to the software’s documentation for accurate and updated instructions.

SPSS Output for Ordinal Logistic Regression Analysis

How to Interpret SPSS Output of Ordinal Logistic Regression

Interpreting the SPSS output for Ordinal Logistic Regression involves understanding various tables and statistics that the software provides. Each table gives insights into different aspects of the regression model. Let’s break down some of the key tables and what they mean:

Model Fitting Information and Goodness-of-Fit Tests

  •    Model Fitting Information: This table provides information on the -2 Log Likelihood of the null model (without predictors) and the final model (with predictors). It also includes the Chi-Square statistic and its significance, which helps in determining if the model with predictors is a better fit than the null model.
  •    Goodness-of-Fit Tests: This includes tests like Pearson and Deviance, which assess how well the model fits the data. A non-significant result (p-value > 0.05) in these tests generally indicates a good fit.

Pseudo R-Square

This table gives measures like Nagelkerke and Cox and Snell R Square, providing an indication of the amount of variance in the dependent variable explained by the model. Higher values indicate a better explanatory power of the model.

Test of Parallel Lines

This test checks the proportional odds assumption, a key assumption in ordinal logistic regression. A non-significant result (p-value > 0.05) means that the assumption holds, and the model is appropriate.

Parameter Estimates

This table is crucial as it provides the estimated coefficients for each predictor and their statistical significance.

– For each predictor, you will see:

  • B (Estimate): The coefficient for the predictor. A positive value indicates that as the predictor increases, the odds of being in a higher category of the outcome variable increase.
  • Standard Error: The standard error of the coefficient estimate.
  • Wald Chi-Square: A test statistic to assess the significance of each predictor.
  • (p-value): The significance level of the predictor. A value less than 0.05 typically indicates a statistically significant predictor.
  • Exp(B) (Odds Ratio): This is the exponentiation of the B coefficient, which provides the odds ratio for a one-unit increase in the predictor.
  • t-values: Indicate how many standard errors the coefficients are from zero. Higher absolute t-values suggest greater significance.
  • P values: Test the null hypothesis that the corresponding coefficient is equal to zero. A low p-value suggests that the predictors are significantly related to the dependent variable.

Model Threshold

This table shows the threshold coefficients for each category of the dependent variable. These thresholds are used to divide the predicted probabilities into categories of the dependent variable.

It’s important to interpret these tables together to get a comprehensive understanding of your Ordinal Logistic Regression model. Look for overall model significance, the significance of individual predictors, the goodness of fit, and the model’s predictive accuracy. Remember, the context of your research and the nature of your data should guide your interpretation.

How to Report Results of Ordinal Logistic Regression in APA

Reporting the results of Ordinal logistic regression in APA (American Psychological Association) format requires a structured presentation. Here’s a step-by-step guide in list format:

  • Introduction: Begin by introducing the purpose of the Ordinal logistic regression analysis and the specific research question or hypothesis you aimed to address.
  • Assumption Check: Briefly mention the verification of assumptions, ensuring the robustness of the ordinal logistic regression analysis.
  • Model Specification: Clearly state the outcome variable (e.g., “The dependent variable, Ordinal Outcome,’ represented whether…”), and list the predictor variables included in the analysis.
  • Model Fit: Report the model fit statistics. Include the Cox & Snell R Square and Nagelkerke R Square values to assess how well the model explains the variation in the ordinal outcome.
  • Predictor Variables: Present a summary of the significant predictor variables included in the final model. Include the variable names, coefficients (Bs), and odds ratios with confidence intervals (e.g., “Variable A (B = 0.543, Odds Ratio = 1.721, 95% CI [1.243, 2.377])”).
  • Overall Model Significance: Indicate whether the overall model was statistically significant using the Likelihood. Include the Chi-Square value and associated p-value (e.g., “The model was statistically significant, χ²(3) = 12.456, p < 0.001”).

Goodness of Fit:

  • Discuss the Pearson and Deviance Test results to assess the goodness of fit. Mention whether the model fits the data well or if there are potential issues (e.g., “Goodness of fit Test indicated a good fit, χ²(7) = 6.245, p = 0.512”).
  • Classification Accuracy: Provide information from the Classification Table, such as the overall classification accuracy percentage and the number of true positives, true negatives, false positives, and false negatives.
  • Hypothesis Testing: Address the research hypotheses by discussing the significance of each predictor variable. Emphasize whether they are associated with the ordinal outcome based on their p-values.
  • Practical Implications: Conclude by discussing the practical significance of the findings and how they contribute to the broader understanding of the phenomenon under investigation.

 

Example of Ordinal Logistic Regression Results in APA Style

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