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A tutorial on Categorical Moderators in MLR

A tutorial on Categorical Moderators in MLR. In this tutorial we’ll work with the Unit 9 homework data and walk through problem 4 of the Unit 9 homework. (*Note: the 2 dummy variables, ‘ manuf ’ and ‘ packag ’ have already been created, so we start by creating the necessary interaction terms).

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A tutorial on Categorical Moderators in MLR

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  1. A tutorial on Categorical Moderators in MLR In this tutorial we’ll work with the Unit 9 homework data and walk through problem 4 of the Unit 9 homework. (*Note: the 2 dummy variables, ‘manuf’ and ‘packag’ have already been created, so we start by creating the necessary interaction terms) Problem 4 of the Unit 9 Homework

  2. Before we can run an MLR with satisfaction, division, and the interaction between satisfaction and division as predictors of job performance, we need to create 2 new interaction variables (corresponding to the 2 dummy variables for division). To do this, go to: Transform Compute Variable Name the target variable ‘satXmanuf’ and then in the Numeric Expression box, indicate that you are multiplying the satisfaction variable by the manuf variable (the manufacturing group dummy variable). This looks like: satisfaction*manuf Click OK

  3. and voila! You have created a new variable that represents half of the interaction between division and satisfaction. Now we create the interaction variable between satisfaction and the 2nd dummy variable, ‘packag’. Taken together, this interaction term AND the satXmanuf interaction term will account for the complete division*satisfaction interaction. Again we go to: Transform Compute Variable In ‘Target Variable’, write satXpackag In Numeric Expression, enter the satisfaction variable, the multiplication symbol (*), and the packag variable (your packaging group dummy variable). It looks like this: satisfaction*packag Click OK

  4. Now we have 2 dummy variables for the division main effect, and 2 interaction terms for the satisfaction by division interaction effect, and we’re ready to run the multiple linear regression analysis. Go to: Analyze Regression  Linear And enter all 5 variable we need: satisfaction manufpackagsatXmanufsatXpackag Click OK

  5. Here is the syntax I used (if you prefer code to ‘point & click’) (*Note, from this window, I just highlight all the text and click the green sideways arrow on top to run the analysis – see the syntax for creating those interaction terms here also)

  6. Here is the output we get in SPSS….

  7. Let’s interpret. Model Summary: R = .541  we cannot say this is the correlation between satisfaction, division, the interaction, and performance – this makes no sense. Instead, we interpret as the correlation between observed and predicted y-values. R Square = .293  this regression model, with division, satisfaction, and the interaction between satisfaction and division, accounts for nearly 30% of the variance in job performance. ANOVA table: F = 3.65 and p = .008  this tells us that our regression model accounts for a significant amount of variance in job performance. We reject our null hypothesis (that our model will NOT predict job performance) and conclude that the combination of division, satisfaction, and the interaction between these variables, significantly predict job performance in this organization. Comparing this output to the output from simple linear regressions (or a MLR with just the main effects of division and satisfaction) tells us that the interaction term is what’s really bringing this model to the significant level. (The main effects are not significant without the interaction). This tells us the interaction between satisfaction and division significantly contributes to this model and significantly predicts job satisfaction. Coefficients: When an interaction is involved, I avoid interpreting the unstandardized coefficients – it gets too convoluted. To really interpret, I jump right to making a graph. But first, let’s look at the t-values for those interaction terms. Note how 1 of the 2 is significant (satXmanuf has a t=3.507 and a p = .001) – this tells me the interaction is significant. We cannot say the interaction between manufacturing and satisfaction is significant but the interaction between satisfaction and packaging is not – this makes no sense because manufacturing and packaging are NOT REAL VARIABLES, but rather dummy variables. Instead, look for one (at least) to be significant and conclude that the entire interaction is significant. Now we’ll use this coefficients table to graph the interaction and interpret…

  8. Now we use the output from SPSS and Excel to graph the interaction. First we write out the full prediction equation, using the unstandardized parameters in the coefficients table: JP = 38.384 – 2.797(sat) – 39.823(manuf) – 12.256(packag) + 9.583(sat*manuf) + 3.894 (sat*packag) *Where JP = job performance, sat = job satisfaction, manuf = manufacturing dummy var., packag = packaging dummy var., sat*manuf = the interaction between job satisfaction and manufacturing dummy var., and sat*packag = the interaction between job satisfaction and packaging dummy var.

  9. JP = 38.384 – 2.797(sat) – 39.823(manuf) – 12.256(packag) + 9.583(sat*manuf) + 3.894 (sat*packag) With this full prediction equation, we can now write equations for each division separately. This way we will have 3 equations with satisfaction predicting performance, 1 for manufacturing, 1 for packaging, and 1 for management. To create these 3 equations, we simply substitute 0’s and 1’s according to our dummy coding scheme. For the manufacturing group, we substitute ‘1’ for the manuf dummy variable and ‘0’ for the packag dummy variable. Manufacturing JP = 38.384 – 2.797(sat) – 39.823(1) – 12.256(0) + 9.583(sat*1) + 3.894 (sat*0) JP = 38.384 – 2.797(sat) – 39.823(1) + 9.583(sat*1) JP = (38.384-39.823) + (9.583-2.797)(sat) JP = -1.439 + 6.786(sat)

  10. JP = 38.384 – 2.797(sat) – 39.823(manuf) – 12.256(packag) + 9.583(sat*manuf) + 3.894 (sat*packag) For the packaging group, we substitute ‘0’ for the manuf dummy variable and ‘1’ for the packag dummy variable. Packaging JP = 38.384 – 2.797(sat) – 39.823(0) – 12.256(1) + 9.583(sat*0) + 3.894 (sat*1) JP = 38.384 – 2.797(sat) – 12.256(1) + 3.894 (sat*1) JP (38.384-12.256) + (3.894-2.797)(sat) JP = 26.128 + 1.097(sat)

  11. JP = 38.384 – 2.797(sat) – 39.823(manuf) – 12.256(packag) + 9.583(sat*manuf) + 3.894 (sat*packag) For the managementgroup, we substitute ‘0’ for the manuf dummy variable and ‘0’ for the packag dummy variable. This one is great because most of the terms are multiplied by 0 and just drop out, making the calculations a snap! Management JP = 38.384 – 2.797(0) – 39.823(0) – 12.256(0) + 9.583(sat*0) + 3.894 (sat*0) JP = 38.384 – 2.797(sat)

  12. Now we have equations for job satisfaction predicting job performance for each of the 3 divisions. We can now easily calculate the job performance score of someone in any division with any score on job satisfaction. We can also use these 3 equations to graph the interaction in Excel by graphing each line (job satisfaction will be on the x-axis, job performance on the y-axis, and each division will have its own line). Manufacturing JP = -1.439 + 6.786(sat) Packaging JP = 26.128 + 1.097(sat) Management JP = 38.384 – 2.797(sat)

  13. A nice way to do this is to calculate the predicted job performance for someone with low satisfaction, medium satisfaction, and high satisfaction for each division. A standard process is to use -1 std. deviation for ‘low satisfaction’, mean for ‘medium satisfaction’ and +1SD for ‘high satisfaction’. Here is the SPSS output for the mean and SD for job satisfaction. We can use this to calculate low, med, and high job satisfaction levels and then plug those in to our division equations and make the graph.

  14. Now, working in Excel, we create a table with the 3 levels of job satisfaction and the 3 divisions. In the table, we calculate the predicted job performance score for someone in each of the 3 divisions with each of the 3 levels of job satisfaction, using the equations we found for each division. As an example, to calculate the value for Manufacturing with Low Sat, I type: =-1.439+6.786*(B14) , because B14 is the cell with the low satisfaction value. To calculate the value for Management with Average Sat, I type: =38.384-2.797*(B15) , because B15 is the cell with the average satisfaction value.

  15. To create the graph, highlight your table and insert a line chart. Make sure Excel knows you want to sort by column and not row…

  16. If your graph looks like THIS, Excel is sorting by row and not column. In the formatting palette, under ‘Chart Data’, it will say “Edit… Sort by” and then give you buttons to click that will sort ‘by row’ or ‘by column’. You want ‘by column’. If all else fails, you can reorganize your table in Excel with each division as a row and each level of job satisfaction as a column.

  17. So this is our final graph. Here’s how we interpret it…. The relationship between job satisfaction and job performance is dramatically different depending on which division an employee is in. For those in the manufacturing division, there is a positive and steep slope, indicating any increase in satisfaction is associated with a relatively large increase in job performance. For those in the packaging division, there is a positive but fairly flat slope, indicating an increase in satisfaction is associated with a relatively slight increase in job performance. For those in the management department, the slope is actually negative, meaning happier managers are the lowest performers. An increase in satisfaction for managers is associated with a decrease in performance. For the organization, they will have to alter their approach to increasing job performance to fit each division. For manufacturing, they can focus on increasing job satisfaction and expect to see a positive impact on performance. For packaging, they can still work towards increasing satisfaction but should also focus effort on another predictor of job performance – perhaps training and support – if they want to see strong gains in performance. For management, the organization should really look into this finding, perhaps with focus groups or interviews. Why is it that highly satisfied managers are low performers? What’s at the root of that unexpected result? Also, what are the other factors that relate to performance? For the management group, a multi-faceted approach to impacting job performance is recommended.

  18. You can also create this graph using the shortcut Excel file: “Graphing_Categorical_Moderation.xls”

  19. In this Excel file, go to the worksheet labeled ‘3 groups’ (because we have 3 groups, the 3 divisions). Fill out the information as follows (see next slide) – all you need is the coefficients table from the MLR output from SPSS. Constant (the intercept) = 38.384 X1 Coefficient (Continuous Independent Variable, job sat in our case ) = -2.797 C1 Coefficient (for 1st dummy variable, manuf in our case) = -39.823 C2 Coefficient (for 2nd dummy variable, packag in our case) = -12.256 X1*C1 Coefficient (interaction btw. job sat and manuf) = 9.583 X1*C2 Coefficient (interaction btw. job sat and packag) = 3.894 Minimum value for X1 (the low job sat value) = 2.97 Maximum value for X1 (the high job sat value) = 5.75 Group names… With ‘1’ on C1 (the group with 1 on the first dummy): Manufacturing With ‘1’ on C2 (the group with a 1 on the 2nd dummy): Packaging With ‘0’ on both C1 and C2 (the comparison group): Management

  20. And the graph will look like this.

  21. With a little editing in Excel (or Powerpoint or Word), it can look like this.

  22. The End

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