Download Example of Sequential Analysis With Moderation, SPSS

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:

Copyright 2014, Karl L. Wuensch - All rights reserved.
Regr-SeqMod.docx
2
Click Run, All. You get this output:
Descriptive Statistics
N
OCB_Org
CSE
Job_Sat
Gender
Age
Ethnicity
Valid N (lis twise)
94
91
90
92
90
92
87
Minimum
22
29
5
1
21
1
Maximum
56
60
25
2
62
4
Mean
42.20
44.70
18.62
1.39
35.91
2.60
Std. Deviation
7.951
7.072
4.357
.491
12.294
.575
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:
Descriptive Statistics
N
OCB_Org
CSE
Job_Sat
Gender
Age
Ethnicity
Valid N (lis twise)
88
87
88
88
88
88
87
Minimum
22
29
5
1
21
1
Maximum
56
60
25
2
62
4
Mean
41.95
44.53
18.58
1.40
36.15
2.63
Std. Deviation
8.006
7.018
4.396
.492
12.331
.553
I delete that one case – (replace “Age” with “CSE”).
We shall need to dummy code the ethnicity variable. Look at its distribution:
3
Ethnicity
Valid
African American (Black)
As ian or Pacific Islander
Caucas ian (White)
His panic or Latino
Total
Frequency
2
30
54
1
87
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.”
4
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:
5
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.
6
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 ZAge ZGender ZAsian ZCaucasian
/METHOD=ENTER ZCSE /METHOD=ENTER Interaction
/METHOD=ENTER ZJob_Sat
.
Regression
Mode l Summ ary
Change St atis tics
Model
1
2
3
4
R
R Square
.491a
.241
.614b
.377
.615c
.379
.642d
.412
Adjust ed
R Square
.204
.339
.332
.360
St d. Error of
the Es timate
.89209537
.81317832
.81730724
.79979741
R Square
Change
.241
.136
.001
.034
F Change
6.516
17.688
.184
4.541
df1
a. Predic tors : (Const ant), ZCaucasian, ZGender, ZAge, ZAsian
b. Predic tors : (Const ant), ZCaucasian, ZGender, ZAge, ZAsian, ZJob_Sat
c. Predic tors : (Const ant), ZCaucasian, ZGender, ZAge, ZAsian, ZJob_Sat, ZCSE
d. Predic tors : (Const ant), ZCaucasian, ZGender, ZAge, ZAsian, ZJob_Sat, ZCSE, Interac tion
df2
4
1
1
1
82
81
80
79
Sig. F Change
.000
.000
.669
.036
7
ANOV Ae
Model
1
2
3
4
Regres sion
Residual
Total
Regres sion
Residual
Total
Regres sion
Residual
Total
Regres sion
Residual
Total
Sum of
Squares
20.742
65.258
86.000
32.438
53.562
86.000
32.561
53.439
86.000
35.466
50.534
86.000
df
4
82
86
5
81
86
6
80
86
7
79
86
Mean Square
5.185
.796
F
6.516
Sig.
.000a
6.488
.661
9.811
.000b
5.427
.668
8.124
.000c
5.067
.640
7.920
.000d
a. Predic tors : (Const ant), ZCaucasian, ZGender, ZAge, ZAsian
b. Predic tors : (Const ant), ZCaucasian, ZGender, ZAge, ZAsian, ZJob_Sat
c. Predic tors : (Const ant), ZCaucasian, ZGender, ZAge, ZAsian, ZJob_Sat , ZCSE
d. Predic tors : (Const ant), ZCaucasian, ZGender, ZAge, ZAsian, ZJob_Sat , ZCSE,
Int erac tion
e. Dependent Variable: ZOCB _Org
8
Coefficientsa
Model
1
2
3
4
(Cons tant)
ZAge
ZGender
ZAsian
ZCaucasian
(Cons tant)
ZAge
ZGender
ZAsian
ZCaucasian
ZJob_Sat
(Cons tant)
ZAge
ZGender
ZAsian
ZCaucasian
ZJob_Sat
ZCSE
(Cons tant)
ZAge
ZGender
ZAsian
ZCaucasian
ZJob_Sat
ZCSE
Interaction
Unstandardized
Coefficients
B
Std. Error
-1.5E-015
.096
.355
.123
-.115
.099
.217
.267
.350
.260
-1.2E-015
.087
.224
.117
-.106
.090
.126
.244
.222
.239
.403
.096
-1.1E-015
.088
.224
.117
-.109
.091
.120
.246
.208
.242
.430
.116
-.046
.108
-.098
.097
.236
.115
-.119
.089
.178
.242
.244
.238
.490
.117
-.093
.108
.181
.085
Standardized
Coefficients
Beta
.355
-.115
.217
.350
.224
-.106
.126
.222
.403
.224
-.109
.120
.208
.430
-.046
.236
-.119
.178
.244
.490
-.093
.193
t
.000
2.877
-1.167
.812
1.344
.000
1.923
-1.173
.518
.926
4.206
.000
1.907
-1.199
.489
.860
3.721
-.429
-1.006
2.054
-1.334
.734
1.027
4.205
-.868
2.131
Sig.
1.000
.005
.247
.419
.183
1.000
.058
.244
.606
.357
.000
1.000
.060
.234
.626
.392
.000
.669
.318
.043
.186
.465
.308
.000
.388
.036
a. Dependent Variable: ZOCB_Org
Here is a presentation of the results:
A sequential multiple regression analysis was employed to build a model for predicting OCBOrg. 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
9
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 OCBOrg 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
10
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.
OCB-Org
Low CSE
Mean CSE
High CSE
Job Satisfaction
Copyright 2013, Karl L. Wuensch - All rights reserved.
Return to Introductory Lesson On Moderation in Multiple Regression.