# Ordinal Regression using SPSS Statistics (cont...)

## Procedure V – Generating odds ratios

Follow the instructions below to generate odds ratios:

1. Click File > New > Syntax on the main menu, as shown below:

Published with written permission from SPSS Statistics, IBM Corporation.

You will be presented with the IBM SPSS Statistics Statistics Syntax Editor window, as shown below:

Published with written permission from SPSS Statistics, IBM Corporation.

2. Make sure that you are working with the correct dataset. You can do this by confirming that the name in brackets after the plum.sav file name in the IBM SPSS Statistics Statistics Data Editor window is the same as selected for the Active: option in the IBM SPSS Statistics Statistics Syntax Editor window, as highlighted below:

Published with written permission from SPSS Statistics, IBM Corporation.

Note: Although the name of the dataset above is "DataSet2", yours might be called something different. This is OK so long as they are the same.

3. To calculate the odds ratios and their 95% confidence intervals in the new file, copy the following highlighted syntax into the Syntax Editor verbatim:

Published with written permission from SPSS Statistics, IBM Corporation.

Explanation: This last stage calculates the odds ratios and their 95% confidence intervals from the parameter estimates and stores these values in new variables within the 'plum' file. To make life simpler, you can copy and paste the following code for this last part: COMPUTE Exp_B = EXP(Estimate).
COMPUTE Lower = EXP(LowerBound).
COMPUTE Upper = EXP(UpperBound).
FORMATS Exp_B Lower Upper (F8.3).
EXECUTE.

4. Click Run > All on the main menu to generate the output, as shown below:

Published with written permission from SPSS Statistics, IBM Corporation.

You will have added some extra columns into your file that represent the odds ratio and its 95% confidence intervals, as highlighted below:

Published with written permission from SPSS Statistics, IBM Corporation.

Having run all five steps of the SPSS Statistics procedures, you should now have all the information you need to start interpreting the results from your ordinal regression.

## Interpreting and Reporting the Ordinal Regression Output

SPSS Statistics will generate quite a few tables of output when carrying out ordinal regression analysis. Below we briefly explain the main steps that you will need to follow to interpret your ordinal regression results. If you want to be taken through all these sections step-by-step, together with the relevant SPSS Statistics output, we do this in our enhanced ordinal regression guide. You can learn more about our enhanced content on our Features: Overview page. First, take a look through these steps:

• Step #1: You need to interpret the results from your assumption tests to make sure that you can use ordinal regression to analyse your data. This includes analysing: (a) the multiple linear regression that you will have had to run to test for multicollinearity (Assumption #3); and (b) the full likelihood ratio test comparing the fitted location model to a model with varying location parameters, as well as the binomial logistic regressions, both of which you will have had to run to test for proportional odds (Assumption #4).
• Step #2: You need to check whether your ordinal regression model has overall goodness-of-fit. This involves interpreting the SPSS Statistics output of a number of statistical tests, including the Pearson and Deviance goodness-of-fit tests; the Cox and Snell, Nagelkerke and McFadden measures of R2; and the likelihood-ratio test. There are advantages and disadvantages to each of these tests, which we discuss in our enhanced ordinal regression guide.
• Step #3: You should determine which of your independent variables (if any) have a statistically significant effect on your dependent variable.
• Step #4a: For categorical independent variables (e.g., "Political party last voted for", which in Great Britain, has 3 groups for this example: "Conservatives", "Labour" and "Liberal Democrats"), you should interpret the odds that one group (e.g., "Conservative" supporters) had a higher or lower value on your dependent variable (e.g., a higher value could be stating that they "Strongly Agree" that "tax is too high" rather than stating that they "Disagree") compared to the second group (e.g., "Labour" supporters). For example, you could look to make a statement such as:

The odds of business owners considering tax to be too high was 1.944 (95% CI, 1.101 to 3.431) times that of non-business owners, a statistically significant effect, Wald χ2(1) = 5.255, p = .022.

In our enhanced ordinal regression guide, we explain how to interpret the parameter estimates that you generated when running the five sets of procedures we took you through in the Procedure section. This will enable you to produce a statement, such as the one above, for your own results.
• Step #4b: For continuous independent variables (e.g., "age", measured in years), you will be able to interpret how a single unit increase or decrease in that variable (e.g., a one year increase or decrease in age), was associated with the odds of your dependent variable having a higher or lower value (e.g., a one year increase in participants' age increasing the odds that they would consider tax to be too high). For example, you could look to make a statement such as:

An increase in age (expressed in years) was associated with an increase in the odds of considering tax too high, with an odds ratio of 1.274 (95% CI, 1.196 to 1.357), Wald χ2(1) = 56.355, p < .001.

Again, in our enhanced ordinal regression guide, we explain how to interpret the parameter estimates that you generated when running the five sets of procedures we took you through in the Procedure section. This will enable you to produce a statement, such as the one above, for your own results.
• Step #5: You will need to determine how well your ordinal regression model predicts the dependent variable, which you can do by looking at the model's predicted probabilities and by generating a confusion table using SPSS Statistics. In our enhanced guide, we show you how to interpret these predicted probabilities, as well as generate and interpret a confusion table using SPSS Statistics.

If you are unsure how to interpret your ordinal regression results, check the assumptions of an ordinal regression or conduct the additional SPSS Statistics procedures required to analyse your data, we show you how to do this in our enhanced ordinal regression guide. We also show you how to write up the results from your assumptions tests and ordinal regression output if you need to report this in a dissertation/thesis, assignment or research report. We do this using the Harvard and APA styles. You can learn more about our enhanced content on our Features: Overview page.

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