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

## Procedure II – Running the PLUM Procedure

The instructions below show you how to run the PLUM procedure. Some of this will require using syntax, but we explain what you need to do. This step produces some of the main results for your ordinal regression analysis, including predicted probabilities, amongst other useful statistical measures we discuss in the Interpretation and Reporting section later.

1. Click Analyze > Regression > Ordinal... on the main menu, as shown below:

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You will be presented with the Ordinal Regression dialogue box, as shown below:

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2. Transfer the ordinal dependent variable – tax_too_high – into the Dependent: box. Next, transfer the categorical independent variables – biz_owner and politics – into the Factor(s) box and the continuous independent variable – age – into the Covariate(s) box, using the appropriate buttons. You will end up with a screen similar to that below:

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Explanation: Ordinal regression can accept independent variables that are either nominal, ordinal or continuous, although ordinal independent variables need to be treated as either nominal or continuous variables. In the Ordinal Regression dialogue box, independent nominal variables are transferred into the Factor(s) box and independent continuous variables are transferred into the Covariate(s) box. You can transfer an ordinal independent variable into either the Factor(s) or Covariate(s) box depending on how you wish the ordinal variable to be treated. However, this is a decision that you need to make.

3. Click on the button and you will be presented with the Ordinal Regression: Options dialogue box, as shown below:

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Note: It is unlikely that you will need to change any of the options in the Ordinal Regression: Options dialogue box shown above. Indeed, in this example you will not change anything. However, if you wanted to change the confidence intervals (the Confidence interval: box) from 95% or change the type of link function (the Link: drop-down box) used, you could do that here.

4. Click on the button and you will be returned to the Ordinal Regression dialogue box.
5. Click on the button and you will be presented with the Ordinal Regression: Output dialogue box, as shown below:

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6. In addition to the options already selected, select Test of parallel lines in the –Display– area. Also, in the –Saved Variables– area, select all four options: Estimated response probabilities, Predicted category, Predicted category probability and Actual category probability. You will end up with a screen similar to below:

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Note 1: When you only have categorical independent variables, you may also want to select Cell information. However, as a general rule, the Cell information option is not very useful when you have continuous independent variables in the model (as in this example).

Note 2: Keeping the default Including multinomial constant option selected in the –Print Log-Likelihood– area results in the FULL log-likelihood being produced, whereas the Excluding multinomial constant option results in the KERNAL of the log-likelihood being produced. This affects the value of the log-likelihood, but not the conclusion. This is explained in our enhanced ordinal regression guide if you are unsure.

7. Click on the button and you will be returned to the Ordinal Regression dialogue box.
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1. Click on the button. You will be presented with the Ordinal Regression: Location dialogue box, as shown below:

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This is where you can specify your model. If you have a model that includes each variable that you entered in the Ordinal Regression dialogue box and you do not have any interactions, you will not need to change anything in this dialogue box. Therefore, in our example, you do not need to make any changes.
2. Click on the button and you will be returned to the Ordinal Regression dialogue box.
3. Click on the button, which will open the Syntax Editor as shown below:

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Explanation: Clicking on the button in any procedure in SPSS Statistics not only opens the syntax editor, but also pastes the command syntax that you have generated by using the point-and-click dialogue boxes. To explain, the dialogue boxes are nothing more than a 'pretty face' that, behind the scenes, generate the command syntax necessary to run statistical tests in SPSS Statistics. This saves most people from ever having to use syntax, which is often considered unfriendly and intimidating. Unfortunately, some statistical test options in SPSS Statistics are not available using the dialogue boxes.

4. For the categorical independent variable with three or more categories (i.e., the politics variable), add the following code to the end of the syntax, but just before the period (full stop):

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Note: The additional syntax shown above is needed to provide an overall test of statistical significance for any categorical independent variable with three or more groups. If you do not have any categorical independent variables that have more than two groups, you can skip this step and go to Step 12 below.

Explanation: If you are familiar with writing (orthogonal) contrasts in SPSS Statistics, the above will be familiar. SPSS Statistics requires as many orthogonal contrasts as there are degrees of freedom (i.e., one less than the number of groups in the independent variable) to provide an omnibus test of statistical significance. The breakdown of this additional syntax is as follows:
/TEST= This is a subcommand that allows you to write customised hypothesis tests or contrasts. The next step is to write down the name of the effect (i.e., the name of the variable) that you are interested in determining an omnibus test statistic for, as shown below: /TEST=politics The categorical independent variable, politics, has more than two groups and, therefore, there needs to be an omnibus test of statistical significance for this variable. The number of values following an effect name is the number of groups in the variable (actually it is the number of parameters, but it amounts to the same thing). As there are three groups in politics, there are three values. These values will either be 1s, 0s or -1s. For the first row, you need to enter a 1 for the first value and a -1 for the last value and enter zeros for all other values (i.e., all values in between the first and last values), followed by a semi-colon, as shown below: /TEST=politics 1 0 -1; On the next line, the pattern is very similar: you re-state the name of the effect and make the last value -1. However, the number 1 is now entered one place to the right compared to the line above. All other values are 0, as shown below: /TEST=politics 1 0 -1;       politics 0 1 -1. Because each line represents a single contrast, the number of rows will equal the number of groups minus 1. In this example, there will be only two rows. Make sure that the final contrast, as shown above, finishes with a period (full stop) and not a semi-colon. By always making the last value -1, having the 1 'travel' one place to the right for each row, and setting all other values to zero, you will get the correct result. To give you a better idea of the pattern that is emerging, consider a variable called transport with four groups, which to get an overall test of statistical significance, would be coded as shown below: /TEST=transport 1 0 0 -1;       transport 0 1 0 -1;       transport 0 0 1 -1. Note all the important features: (i) the name of the variable is declared; (ii) there are as many (horizontal) values as there are groups of the variable; (iii) a semi-colon finishes all lines except the last, which has a period (full stop); (iv) there are only 1s, 0s and -1s; (v) the last value is always -1; (vi) the first value of the first line starts with 1; (vii) the 1 'travels' to the right one place at a time (i.e., one place for every line); and (viii) the number of lines is one less than the number of groups (representing the number of degrees of freedom). Although there are other methods of achieving an omnibus statistical test, the above method is easily followed and this allows less mistakes to be made.

As a final point, you can run more than one omnibus statistical test at the same time; you just need to make multiple /TEST statements with the period (full stop) only at the end of the last contrast/line. For example, if running both politics and transport, you would have: /TEST=politics 1 0 -1;       politics 0 1 -1 /TEST=transport 1 0 0 -1;       transport 0 1 0 -1;       transport 0 0 1 -1. Notice that the only change is that the period (full stop) is missing from the last contrast/line for politics.

5. Click Run > All on the main menu, as shown below. This will generate the output.

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## Procedure III – Outputting the PLUM parameters estimates using OMS

Now that you have run the PLUM procedure, you can go back to the OMS control panel and get SPSS Statistics to output the file containing the Parameter Estimates table's information that has been stored in memory.

1. Click Utilities > OMS Control Panel... on the main menu, as shown below:

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You will be presented you with the Output Management System Control Panel dialogue box with your prior selected request, as shown below:

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2. Click on the button. This will change the Status column to "end" in the Requests box, as highlighted below:

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3. Click on the button. You will be presented with the OMS Control Panel: Summary dialogue box, as shown below:

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4. Click on the button and to exit.

## Procedure IV – Saving the newly-created file

If you have followed the procedure above, you will not only have generated the output in the usual way (i.e., in the Output Viewer window), but you will have also created a new SPSS Statistics data file, as shown below:

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This file contains the odds ratios and their 95% confidence intervals, but it is not currently saved. Therefore, save the file by clicking on
File > Save As... on the main menu (as shown below) and saving the file with a name of your choosing in a directory of your choosing (it is saved as plum.sav in this guide).

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Now that you have saved the file, you can add odds ratios to the file. To do this, follow the steps in the next section, Procedure V – Generating odds ratios, on the next page.