Sequential Moderated Multiple Regression Analysis

Sequential Moderated Multiple Regression Analysis

Graduate student Chris Jewett wishes to predict OCB-Org, a measure of the organizational citizenship behavior show by an individual (directed towards the organization; another subscale measures OCB directed towards other individuals in the organization). He wishes to use a sequential analysis. In the first step the demographic predictors will be entered. They are gender, age, and ethnicity. In the second step job satisfaction will be entered. In the third step core self evaluation will be entered. The fourth and final step will investigate a possible interaction between job satisfaction and core self evaluation.

The data set is available on my SPSS Data Page with the name Regr-SeqMod.sav.

I decided to standardize all of the variables. The metric of the variables here is not intrinsically meaningful to me.

SPSS will standardize the variables for me, but first I must remove any cases with missing data on the variables to be standardized. Descriptive statistics shows that there are missing data. Click Analyze, Descriptive Statistics, Descriptives. Scoot all of the variables into the Variables pane and click the “Paste” button.

Normally you would click the OK button, but we want to make SPSS open a syntax window, into which we shall paste and run syntax.

The syntax window should now look like this:

Click Run, All. You get this output:

JobSat and Age have the greatest frequencies of missing data, so I’ll start by removing all cases with missing data on Job_Sat. I paste the following syntax in the syntax window, select it, and then click “Run Selection.”

filter off.

use all.

select if(not missing(Job_Sat)).

execute.

Next I do the same with Age – just replace “Job_Sat” with “Age” and run the syntax again.

Now the descriptive statistics shows that the only variable still with missing data is CSE:

I delete that one case – (replace “Age” with “CSE”).

We shall need to dummy code the ethnicity variable. Look at its distribution:

With only three cases that are neither Asian/Pacific Islander nor Caucasian, I probably should just discard those cases, but for pedagogical purposes I shall keep them and create a pair of dummy variables which code for three groups (Asian/Pacific, Caucasian, Other).

If you look back at the Variable Labels you will see that African American is coded as 1, Asian as 2, Caucasian as 3, and Hispanic as 4.

Dummy variable “Asian” gets value 1 for all those who indicated their ethnicity was Asian/Pacific, all others get a value of 0. Click Transform, Recode into Different Variables. Select Ethnicity, name the new variable “Asian,”

and click “Old and New Values.”

Click Continue, OK.

In similar fashion I create dummy variable “Caucasian,” with value 1 for those who indicated their ethnicity was Caucasian and value 0 for all others.

Next I run the descriptive statistics again on all of the predictors (including the dummy variables), but this time I check the box “Save standardized variables as variables.”

A peek back at the data sheet shows that the standardized variables have been added:

Now I create the interaction term as the product of standardized Job_Sat and standardized CSE. Click Transform, Compute:

Now for the regression analysis.

Click Analyze, Regression, Linear. Scoot ZOCB_Org into the Dependent box and ZAge, ZGender, ZAsian, and ZCaucasian into the Independents box.

Click Next. The Independents box will clear and the window will indicate “Block 2 of 2.”

Scoot ZJob_Sat into the Independents box and click Next.

Scoot ZCSE into the Independents box and click Next.

Scoot Interaction into the Independents box. You have now defined the four steps of the sequential analysis.

Click Statistics and ask for (in addition to the defaults), R Squared Change. Continue, OK.

Here is the statistical output:

REGRESSION

/MISSING LISTWISE

/STATISTICS COEFF OUTS R ANOVA CHANGE

/CRITERIA=PIN(.05) POUT(.10)

/NOORIGIN

/DEPENDENT ZOCB_Org

/METHOD=ENTER ZAgeZGenderZAsianZCaucasian /METHOD=ENTER ZJob_Sat

/METHOD=ENTER ZCSE /METHOD=ENTER Interaction .

Regression

Here is a presentation of the results:

A sequential multiple regression analysis was employed to build a model for predicting OCB-Org. In the first step three predictors were added: Ethnicity (represented by two dummy variables), gender (1 for female, 2 for male), and age (a continuous variable). This model was statistically significant, F(4, 82) = 6.516, p < .001, R2 = .241, CI.95 = .069, .378. As shown in Table 1, only age had a significant unique effect, with OCB-Org increasing with age.

Job satisfaction was entered in the second step. Addition of this predictor significantly increased the fit of the model to the data, F(1, 81) = 17.688, p < .001), sr2 = .136. The resulting model R2 was significantly greater than zero, F(5, 81) = 9.811, p < .001, R2 = .377, CI.95 = .177, .506.

The third step consisted of adding CSE-total. Addition of this predictor did not significantly increase the model R2, F(1, 80) = 0.181, p = .67, sr2 = .001. The resulting model R2 was significantly greater than zero, F(6, 80) = 8.124, p < .001, R2 = .379, CI.95 = .169, .502.

The fourth and final step consisted of adding an interaction term, coding the interaction between job satisfaction and CSE-total. Addition of the interaction term did significantly increase the model R2, F(1, 79) = 4.541, p = .036, sr2 = .034. The resulting model R2 was significantly greater than zero, F(7, 79) = 7.920, p < .001, R2 = .412, CI.95 = .193, .527. The final model (with all variables standardized) was OCB-Org = .236Age - .119Gender + .244White + .178Asian + .490Job Satisfaction - .093CSE-Total + .194Interaction.

The interaction is illustrated in Figure 1, where the relationship between Job Satisfaction and OCB-Org is plotted for low CSE-Total (one standard deviation below the mean), mean CSE-Total, and high CSE-Total (one standard deviation above the mean). The effect of job satisfaction on OCB-Org increases as CSE-Total increases.

Table 1. Predicting OCB-Org From the Demographic Variables

Predictor / Beta / p
Age / .355 / .005
Gender / .115 / .247
White Ethnicity / .350 / .183
Asian Ethnicity / .217 / .419

Illustrating the Interaction

Get three regression lines (at low, mean, and high CSE-Total). Keep the demographics at their mean value, which is zero (since they are standardized), so they drop out of the prediction equation.

OCB-Org = .49Job Satisfaction - .093CSE-Total + .194Interaction

Low CSE (CSE = -1)

OCB-Org = .49Job Satisfaction - .093(-1) + .194(-1)Job Satisfaction

= .296Job Satisfaction +.093

Mean CSE (CSE = 0)

OCB-Org = .49Job Satisfaction - .093(0) + .194(0)Job Satisfaction

= .49Job Satisfaction

High CSE (CSE=1)

OCB-Org = .49Job Satisfaction - .093(1) + .194(1)Job Satisfaction

= .684Job Satisfaction - .093

For each of these three levels of CSE, predict two values of OCB-Org, one at Low Job Satisfaction (-1), one at high satisfaction (+1). Then plot the three lines.

Low CSE, Low JS: OCB = -.296 +.093 = -.203

Low CSE, High JS: OCB = .296 + .093 = .389

Mean CSE, Low JS: OCB = -.49

Mean CSE, High JS: OCB = .49

High CSE, Low JS: OCB = -.684 - .093 = -.777

High CSE, High JS: OCB = .684 -.093 = .591

I used Microsoft Graph to produce the plot below.

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