Graphing Interactions Using the PROCESS Macro in SPSS

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Christine R. Wells, Ph.D.

UCLA Office of Advanced Research Computing

Statistical Methods and Data Analytics

Introduction

•

We will cover only some of what can be done in the PROCESS macro

in SPSS.

•

We will focus on moderation models (no mediation).

•

We will be using version 4.0 of the PROCESS macro.

•

Information about the PROCESS macro can be found at

•

Much of the material in this workshop is based on 

Introduction to

Mediation, Moderation and Conditional Process Analysis: A

Regression-based Approach, Third Edition

 by Andrew F. Hayes (2022).

Installing PROCESS

•

Go to 

processmacro.org

 and then to the Downloads tab (at the top of

the page).

•

Download the zipped file, and then unzip the file.

•

Read the Installing PROCESS custom dialog PDF.

•

Finally, open and run the process.sps file.

•

The custom dialog will remain installed as you open and close the

SPSS program, but you must run the process.sps file each time you

open SPSS and want to use the PROCESS macro.

Download the datasets

•

Please go to the 

webpage

 and download the datasets

hsbmoderation.sav and exercise.sav.

•

Save them somewhere that it is easy for you to access (such as C:\).

•

NOTE:  SPSS will allow long variable names, but PROCESS has trouble

with variable names longer than eight characters.  To avoid these

potential difficulties, the names of all variables used in the examples

are eight characters or less.

Getting the SPSS commands in the log file

•

Log file = output file

•

Some versions of SPSS have the syntax echoed in the output by

default.

•

If you don’t see SPSS syntax above the output, click on Edit, Options,

the Viewer tab, and then click to check the box in lower left corner to

Display the Commands in the Log.

Definition of interaction term

•

Interaction terms are common in regression models.

•

Without an interaction term in a regression model, the effect of one

predictor on the outcome is independent of all other predictors in the

model.

•

The interaction term is the product of two predictors.

•

The inclusion of an interaction term in a regression model means that

the effect of one predictor on the outcome depends on the level of

the other predictor.

Definition of interaction term (continued)

•

Interaction terms are symmetric: the effect of Predictor A on the

outcome depends on the level of Predictor B, and the effect of

Predictor B on the outcome depends on the level of Predictor A.

•

For simplicity, some authors refer to one predictor as “the predictor”

and the other as “the moderator”.

•

The important thing to remember is that those names are used only

to help people; there is no difference mathematically and your

statistical software does not care what you call any of the predictors.

In this workshop

•

You will learn how to interpret the coefficients of the interaction

terms and the lower-order effects (to be explained later), how to

probe the interaction and how to graph it.

•

Many researchers find the interpretation of the coefficients of the

interaction terms to be difficult, so they simply report whether or not

the term is statistically significant and then present the graph of the

interaction.

SPSS procedures to run linear regression

•

There are many procedures that can be used to run linear regression

analyses in SPSS, e.g., REGRESSION, GLM, MIXED, LINEAR.

•

However, most procedures that run regression analyses in SPSS lack

the ability to graph interactions.

•

One exception to this is the GLM command, which can graph binary-

by-binary interactions.

•

This is a big limitation, so we will use PROCESS to graph interactions

that SPSS can’t.

Graphing interactions with PROCESS

•

The PROCESS macro, written by Andrew Hayes, provides a way to get

the information necessary to graph a variety of different types of

interactions, including binary-by-binary, binary-by-continuous,

continuous-by-continuous, two two-way interactions in a model and

even three-way interactions.

•

This workshop will focus on graphing different types of interactions in

linear regression models.

The datasets

•

Hsbmoderation

•

outcome = opinion

•

predictors = detail, age, etc.

•

Exercise

•

outcome = loss

•

predictors = hours, effort, female

DATASET NAME and DATASET ACTIVATE

•

Before we start using the PROCESS macro, we need to quickly discuss

some SPSS commands that we will need to keep everything running

correctly.

•

The SPSS command DATASET NAME is used to name a dataset that

has been created (but not necessarily saved anywhere).

•

The SPSS command DATASET ACTIVATE makes active a particular

dataset, and this will be used to ensure that the correct dataset is

active just before we execute the SPSS syntax.

The GET FILE command

•

The get file command is used to open an SPSS dataset.

•

We will issue the DATASET NAME command immediately after the GET FILE

command so that we can activate the dataset when we need it.

get file

"D:\data\Seminars\Graphing_Interactions_SPSS_PROCESS\hsbmoderation.sav".

dataset name hsbm.

get file

"D:\data\Seminars\Graphing_Interactions_SPSS_PROCESS\exercise.sav".

dataset name exercise.

Binary by binary interactions

Interaction and lower-order terms

•

The interaction term is the product of two predictors, 

binaryvr

  and

bcovar

.

•

The variables 

binaryvr

  and 

bcovar

 will also be included in the model;

they are called “lower-order” terms.

•

Their presence in the model is necessary to make the coefficient of

the interaction term interpretable.

•

Hence there are three predictor variables:  

binaryvr

, 

bcovar

 and their

interaction.

•

Do not use recoded versions of the lower-order effects.

Conceptual diagram

W

W

X

X

Y

Y

Statistical model

X

X

W

W

XW

XW

Y

Y

Using the SPSS GLM command

glm opinion by binaryvr bcovar

    /design binaryvr bcovar binaryvr*bcovar

    /print parameter

    /emmeans = tables(binaryvr*bcovar)

    /plot = profile(binaryvr*bcovar) errorbar = se.

•

By default, SPSS uses the highest-numbered category as the reference

group, and this default cannot be changed.

SPSS GLM output

SPSS GLM output

SPSS GLM output

SPSS GLM output

Interpretation

•

The overall model is not statistically significant (from the table of

Tests of Between Subjects Effects, p = 0.357).  Because of this,

interpretation of the rest of the output would normally cease.

However, for this example, let’s continue.

•

Given that the overall model is not statistically significant, it should

not be surprising that the R-squared value is small (below the table of

Tests of Between Subjects Effects, R-squared = 0.016).

•

In the table of Parameter Estimates, we find the unstandardized

coefficients (called B) and their standard errors, the t test statistics,

the p-values (in the column Sig.) and the 95% CIs.

Interpretation

•

The coefficient of 53.883 for the intercept (AKA constant) is the

expected value of the outcome variable (

opinion

) when all of the

predictors in the model are held at 0.  In this model, 0 is a reasonable

value for both predictors, 

binaryvr

 and 

bcvoar

.

•

However, in many models, 0 is not in the range of one or more of the

predictor variables, and the expected value of the outcome may not

be in the range of the outcome variable.  In such situations,

researchers should report the coefficient for the intercept but not

interpret it. (pages 242-245)

Interpetation

•

The coefficient of -1.097 for 

binaryvr

 is the effect of 

binaryvr

 when 

bcovar

= 1.  Because the coefficient is negative, we know that this predictor

variable and the outcome are negatively associated (given this model; the

coefficient may have a different sign in a different model).

•

Hence, we would say that for a one-unit increase in 

binaryvr

, the expected

change (or decrease) in the outcome is approximately 1 unit, holding all

other variables in the model constant.

•

Because 

binaryvr

 has only two values, 0 and 1, we can also say that the

difference between these two groups is approximately 1 unit when 

bcovar

= 1.  Because this coefficient is not statistically significant, in practice, we

would not interpret it; in fact, it may be 0.

Interpetation

•

In some research situations, this value may be of interest, and in

other research situations, it will not be.

•

Researchers should always report the coefficient, but it is the

researcher’s decision whether or not to interpret this value.

•

The coefficient for 

bcovar

 is 2.167.  This is the effect of 

bcovar

 when

binaryvr

 = 1.  Again, it is not statistically significant, so, in practice,

this coefficient would not be interpreted, but it is the difference

between the group coded 0 and the group coded 1 when 

binaryvr

 is

equal to 1.

•

Both of these coefficients are called simple effects or conditional

effects. (page 254)

Caution!

•

Remember that these coefficients are simple effects.

•

When writing about these lower-order terms, the phrases “main

effects” and “average effects” should be avoided.

•

NOTE:  The term “main effect” comes from ANOVA.  It is used

because the coding of the lower-order effects is different in ANOVA

than in regression.

Interpetation

•

The coefficient for the interaction term is -3.877 and is not statistically

significant (p = 0.353).

•

This coefficient describes how much the difference in the outcome,

opinion

, between two cases that differ by one unit on 

binaryvr

changes as 

bcovar

 changes by one unit, and vice versa.

•

Because this is difficult for many researchers and consumers of

research to understand, graphs are particularly helpful.

Graph of interaction

•

This example was used because the graph apparently shows a “cross-over” interaction, but notice the size of the error bars.

Both error bars cover both points on both sides, and this is another way of showing that the interaction is statistically non-

significant.

Try it yourself

•

What is the difference between a dichotomous variable and a binary

variable?

•

Why would this matter in a regression analysis?

•

Given that the interaction term is not statistically significant, should

the interaction term remain in the model or be removed?

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Notice that 

binaryvr

 and 

bcovar

 come after 

with

; notice change to

the reference group.

•

Notice that the emmeans and plot subcommands have been

removed.  Those subcommands can only be used with variables that

follow the SPSS keyword 

by

.

glm opinion with binaryvr bcovar

    /design binaryvr bcovar binaryvr*bcovar

    /print parameter.

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Binary by binary interaction with PROCESS

process y = opinion /x = binaryvr /w = bcovar /model = 1 /plot = 1.

•

To run a moderation model, (at least) three variables need to

specified:  y, which is the outcome; x, which is one of the predictors;

and w, which is the other predictor and also called the moderator.

•

The model number must be specified, and for this model, we specify

model 1.  Models 1, 2 and 3 are moderation models (with no

mediation).

•

We add the plot = 1 subcommand to add to the output the SPSS

syntax needed for creating the graph of the interaction.

PROCESS output

Model  : 1

    Y  : opinion

    X  : binaryvr

    W  : bcovar

Sample

Size:  200

PROCESS output

OUTCOME VARIABLE:

 opinion

Model Summary

          R          R-sq        MSE              F              df1          df2                 p

      .1277      .0163      115.1128     1.0832     3.0000   196.0000      .3573

Model

                    coeff           se            t                    p           LLCI          ULCI

constant    51.0260     1.2227    41.7325      .0000     48.6147     53.4373

binaryvr     4.9740      3.1173     1.5956        .1122    -1.1737      11.1217

bcovar       1.7103      1.6613     1.0295        .3045     -1.5660      4.9866

Int_1         -3.8770      4.1686     -.9300        .3535    -12.0981     4.3442

PROCESS output

Product terms key:

 Int_1    :        binaryvr x        bcovar

Test(s) of highest order unconditional interaction(s):

              R2-chng   F           df1          df2                 p

X*W      .0043      .8650     1.0000   196.0000      .3535

PROCESS output

    Focal predict: binaryvr (X)

          Mod var: bcovar   (W)

Data for visualizing the conditional effect of the focal predictor:  Paste text below into a SPSS syntax window and

execute to produce plot.

DATA LIST FREE/

   binaryvr   bcovar     opinion    .

BEGIN DATA.

      .0000      .0000    51.0260

     1.0000      .0000    56.0000

      .0000     1.0000    52.7363

     1.0000     1.0000    53.8333

END DATA.

GRAPH/SCATTERPLOT=

 binaryvr WITH     opinion  BY       bcovar   .

PROCESS output

*********************** ANALYSIS NOTES AND ERRORS ************************

Level of confidence for all confidence intervals in output:

  95.0000

------ END MATRIX -----

SPSS syntax to graph interaction

DATA LIST FREE/

   binaryvr   bcovar     opinion    .

BEGIN DATA.

     1.0000      .0000    51.0260

     2.0000      .0000    56.0000

     1.0000     1.0000    52.7363

     2.0000     1.0000    53.8333

END DATA.

GRAPH/SCATTERPLOT=

 binaryvr WITH     opinion  BY       bcovar   .

Resulting graph

Graph after using graph editor

GPL syntax

GGRAPH

  /GRAPHDATASET NAME="GraphDataset" VARIABLES= opinion bcovar binaryvr

  /GRAPHSPEC SOURCE=INLINE.

BEGIN GPL

SOURCE: s=userSource( id( "GraphDataset" ) )

DATA: opinion=col( source(s), name( "opinion" ) )

DATA: bcovar=col( source(s), name( "bcovar" ), unit.category() )

DATA: binaryvr = col(source(s), name("binaryvr"), unit.category())

GUIDE: axis( dim( 1 ), label( "binaryvr" ) )

GUIDE: axis( dim( 2 ), label( "opinion" ) )

ELEMENT: point( position( binaryvr * opinion )) , shape(bcovar))

ELEMENT: line(position(smooth.linear(binaryvr * opinion)), shape(bcovar))

END GPL.

Comments about GGRAPH and GPL

•

The GRAPH command given in the PROCESS output is from the legacy

dialogs in the point-and-click interface.

•

GGRAPH and GPL are from the Chart Builder and are the newer

graphing commands.

•

For more information about using GPL to customize your graphs,

please see

https://www.ibm.com/docs/en/SSLVMB_28.0.0/pdf/GPL_Reference_

Guide_for_IBM_SPSS_Statistics.pdf

 and

https://stats.oarc.ucla.edu/spss/library/spss-librarymaking-graphs-

with-the-ggraph-command-and-gpl/

Comments on GPL

•

Note that GPL is unlike SPSS syntax in that the statements must be in

a particular order and are case sensitive.

•

If you want to make a graph appropriate for publication, you probably

need to use GPL.

•

GPL is similar to the way graphs are made in R using ggplot2.

Binary by three-level interaction

SPSS GLM syntax for binary by three-level

dataset activate hsbm.

glm opinion by binaryvr detail3

    /design = binaryvr detail3 binaryvr*detail3

    /print = parameter

    /emmeans = tables(binaryvr*detail3)

    /plot = profile(binaryvr*detail3) errorbar = se.

SPSS GLM output

SPSS GLM output

SPSS GLM output

SPSS GLM output

PROCESS syntax for binary by three-level

dataset activate hsbm.

process y = opinion /x = binaryvr /w = detail3 /mcw = 1 /model = 1

/plot = 1.

Notice that the mcw = 1 subcommand has been added.  This indicates

that the 

w

 variable is 

m

ulti

c

ategorical.

PROCESS output

Model  : 1

    Y  : opinion

    X  : binaryvr

    W  : detail3

Sample

Size:  200

Coding of categorical W variable for analysis:

 detail3      W1      W2

    .000    .000    .000

   1.000   1.000    .000

   2.000    .000   1.000

•

PROCESS output

Model Summary

          R          R-sq        MSE           F                df1           df2                 p

      .5673      .3218      80.1780    18.4132     5.0000   194.0000      .0000

Model

                   coeff           se               t                 p            LLCI           ULCI

constant    43.9804     1.2538     35.0765      .0000    41.5075    46.4533

binaryvr     3.2696       4.6494        .7032      .4828    -5.9002      12.4394

W1           

7.3696     

1.7054     

4.3213      .0000     4.0061    

10.7331

W2         

 15.7389     

1.7259    

 9.1192     .0000    12.3350    19.1429

Int_1          -1.2863       5.3196      -.2418      .8092   -11.7779     9.2054

Int_2          -4.2197      5.4028      -.7810      .4357   -14.8755      6.4362

Product terms key:

 Int_1    :        binaryvr x        W1

 Int_2    :        binaryvr x        W2

Test(s) of highest order unconditional interaction(s):

           R2-chng          F        df1           df2                 p

X*W      .0031      .4425     2.0000   194.0000      .6431

SPSS syntax to graph interaction

DATA LIST FREE/

   binaryvr   detail3    opinion    .

BEGIN DATA.

     1.0000      .0000    43.9804

     2.0000      .0000    47.2500

     1.0000     1.0000    51.3500

     2.0000     1.0000    53.3333

     1.0000     2.0000    59.7193

     2.0000     2.0000    58.7692

END DATA.

GRAPH/SCATTERPLOT=

 binaryvr WITH     opinion  BY       detail3  .

Graph of binary by three-level interaction

Try it yourself

•

What if the X variable had three levels instead of the W variable?

•

Write the PROCESS syntax for that model using the hsbmoderation

dataset.

Binary by continuous interaction

SPSS GLM syntax for binary by continuous

dataset activate hsbm.

glm opinion with age binaryvr

    /design = age binaryvr age*binaryvr

    /print = parameter.

SPSS GLM output

SPSS GLM output

Interpretation

•

The overall model is statistically significate (p < 0.001).

•

 The intercept is 13.672, which is the expected value of the outcome

(

opinion

) when all predictors equal 0 (whether that is realistic or not).

•

The coefficient for 

age

 is 0.733 and is the effect of 

age

 when 

binaryvr

equals 0 (because we used with keyword 

with

).  It is a simple slope.

•

The coefficient for 

binaryvr

 is 31.319 and is the effect of 

binaryvr

 when

age

 equals 0 (even though that is not a value in the dataset).  It is a simple

effect.

•

The coefficient of the interaction term is -0.556 and shows how much the

difference in 

opinion

 between two cases that differ by one unit on 

age

changes as 

binaryvr

 changes by one unit (AKA goes from 0 to 1). (pages

254-255)

PROCESS syntax for binary by continuous

dataset activate hsbm.

process y = opinion /x = age /w = binaryvr /model = 1 /plot = 1.

PROCESS output

Model Summary

      R              R-sq      MSE           F                df1           df2                 p

      .6211      .3858    71.8766    41.0350     3.0000   196.0000      .0000

Model

                   coeff            se             t                p            LLCI          ULCI

constant    13.6720     3.5635     3.8367      .0002     6.6442    20.6997

age                  .7326       .0670    10.9280      .0000      .6004       .8649

binaryvr     31.3192   12.3956     2.5266      .0123     6.8734    55.7651

Int_1              -.5563       .2224    -2.5012      .0132     -.9950       -.1177

Product terms key:

 Int_1    :        age      x        binaryvr

Test(s) of highest order unconditional interaction(s):

           R2-chng    F               df1          df2                 p

X*W      .0196     6.2560     1.0000   196.0000      .0132

PROCESS output

 Focal predict: age      (X)

          Mod var: binaryvr (W)

Conditional effects of the focal predictor at values of the moderator(s):

   binaryvr     Effect         se             t                  p          LLCI        ULCI

      .0000      .7326      .0670    10.9280      .0000      .6004      .8649

     1.0000     .1763      .2121        .8313      .4068     -.2420      .5946

SPSS syntaxt to graph interaction

DATA LIST FREE/

   age        binaryvr   opinion    .

BEGIN DATA.

    41.0000      .0000    43.7102

    54.0000      .0000    53.2345

    62.0000      .0000    59.0956

    41.0000     1.0000    52.2194

    54.0000     1.0000    54.5113

    62.0000     1.0000    55.9217

END DATA.

GRAPH/SCATTERPLOT=

 age      WITH     opinion  BY       binaryvr .

Graph of binary by continuous interaction

Howa are the values age calculated?

•

Where do the values of age of 41, 54 and 62 come from?

•

They are the 16th, 50th and 84th percentile.

dataset activate hsbm.

freq var = age

    /statistics = median

    /percentiles = 16.0 84.0

    /format = notable.

How are the values of effect calculated?

•

b

1

 + b

3

w = effect

•

b

1

 = 0.736 (the coefficient for 

age

)

•

b

3

 = -0.5563 (the coefficient for the interaction term)

•

Effect 0.7326 = 0.7326 + 0.5563*(0)

•

Effect 0.1763 = 0.7326 - 0.5563*(1)

Continuous by three-level interaction

Continuous by three-level interaction

dataset activate hsbm.

glm opinion with age by detail3

    /design = age detail3 age*detail3

    /print = parameter.

SPSS GLM output

SPSS GLM output

PROCESS syntax for continuous by three-level

dataset activate hsbm.

process y = opinion /x = age /w = detail3 /mcw = 1 /model = 1 /plot = 1

/intprobe = 1.

•

The intprobe subcommand is used because, by default, PROCESS only

probes statistically significant interactions.  Including intprobe = 1

includes the probe of the interaction regardless of statistical

significance.

PROCESS output

Model

                   coeff           se              t                p            LLCI          ULCI

constant    22.7467     6.4785     3.5111      .0006     9.9693    35.5241

age                  .4716       .1403     3.3627      .0009       .1950         .7482

W1          

 6.7582    

 8.4559      .7992      .4251    -9.9191    23.4356

W2            

.8812    11.4381      .0770      .9387   -21.6779    23.4403

Int_1              -.0462        .1736     -.2660      .7906      -.3887        .2963

Int_2               .1371        .2120      .6469      .5185      -.2809         .5552

Product terms key:

 Int_1    :        age      x        W1

 Int_2    :        age      x        W2

Test(s) of highest order unconditional interaction(s):

              R2-chng   F            df1          df2                p

X*W      .0027      .4711     2.0000   194.0000      .6250

PROCESS output

 Focal predict: age      (X)

          Mod var: detail3  (W)

Conditional effects of the focal predictor at values of the moderator(s):

    detail3      Effect          se             t                p           LLCI         ULCI

      .0000      .4716      .1403     3.3627      .0009      .1950      .7482

     1.0000      .4254      .1024     4.1552      .0000      .2235      .6274

     2.0000      .6087      .1589     3.8304      .0002      .2953      .9222

PROCESS output

Data for visualizing the conditional effect of the focal predictor:

Paste text below into a SPSS syntax window and execute to produce plot.

DATA LIST FREE/

   age        detail3    opinion    .

BEGIN DATA.

    41.0000      .0000    42.0830

    54.0000      .0000    48.2141

    62.0000      .0000    51.9870

    41.0000     1.0000    46.9477

    54.0000     1.0000    52.4784

    62.0000     1.0000    55.8819

    41.0000     2.0000    48.5857

    54.0000     2.0000    56.4992

    62.0000     2.0000    61.3690

END DATA.

GRAPH/SCATTERPLOT=

 age      WITH     opinion  BY       detail3  .

Graph of interaction

Interpretation

•

The overall model is statistically significate (p < 0.001).

•

 The intercept is 

22.7467

, which is the expected value of the outcome

(

opinion

) when all predictors equal 0 (whether that is realistic or not).

•

The coefficient for 

age

 is 0.4716 and is the effect of 

age

 when 

detail3

 is at

its reference group.  The reference group is different in GLM and PROCESS.

It is a simple effect.

•

The coefficient for 

w1

 is 

6.7582

 and is the effect of 

w1

 compared to the

reference group when 

age

 equals 0 (even though that is not a value in the

dataset).  It is a simple effect.

•

The coefficient for 

w2

 is 0

.8812

 and is the effect of 

w2

 compared to the

reference group when 

age

 equals 0 (even though that is not a value in the

dataset).  It is a simple effect.

Interpretation

•

The coefficient of the interaction term 

int_1

 is -0.0462 and shows

how much the difference in 

opinion

 between two cases that differ by

one unit on 

age

 changes as 

detail3

 changes by one unit.

•

The coefficient of the interaction term 

int_2

 is 0.1371 and shows how

much the difference in 

opinion

 between two cases that differ by one

unit on 

age

 changes as 

detail

 changes by one unit.

Contiuous by continuous interaction

PROCESS syntax for continuous by continuous

dataset activate exercise.

process y = loss /x = hours /w = effort /model = 1 /plot = 1.

PROCESS output

Model  : 1

    Y  : loss

    X  : hours

    W  : effort

Sample

Size:  900

•

PROCESS output

OUTCOME VARIABLE:

 loss

Model Summary

      R              R-sq        MSE             F                df1          df2                 p

      .2796      .0782      183.8871    25.3295     3.0000   896.0000      .0000

Model

                    coeff         se               t               p            LLCI            ULCI

constant     7.7986    11.6036      .6721      .5017     -14.9748    30.5721

hours         -9.3757     5.6639     -1.6553     .0982     -20.4918      1.7404

effort           -.0803       .3846       -.2087      .8347         -.8352        .6746

Int_1             .3933       .1875      2.0978      .0362          .0253        .7613

Product terms key:

 Int_1    :        hours    x        effort

Test(s) of highest order unconditional interaction(s):

            R2-chng   F              df1          df2                 p

X*W      .0045     4.4008     1.0000   896.0000      .0362

PROCESS output

 Focal predict: hours    (X)

          Mod var: effort   (W)

Conditional effects of the focal predictor at values of the moderator(s):

       effort        Effect          se              t                p            LLCI          ULCI

    24.5391       .2767     1.3467       .2055      .8373    -2.3663     2.9197

    29.6340     2.2808       .9152     2.4920      .0129       .4845     4.0771

    34.7141     4.2790     1.2969     3.2994      .0010     1.7336     6.8243

PROCESS output

DATA LIST FREE/

   hours      effort     loss       .

BEGIN DATA.

     1.5165    24.5391     6.2483

     2.0051    24.5391     6.3835

     2.4859    24.5391     6.5165

     1.5165    29.6340     8.8784

     2.0051    29.6340     9.9930

     2.4859    29.6340    11.0894

     1.5165    34.7141    11.5008

     2.0051    34.7141    13.5919

     2.4859    34.7141    15.6489

END DATA.

GRAPH/SCATTERPLOT=

 hours    WITH     loss     BY       effort   .

PROCESS output

Level of confidence for all confidence intervals in output:

  95.0000

W values in conditional tables are the 16th, 50th, and 84th percentiles.

Graph of interaction

Interpretation

•

The overall model is statistically significate (p = 0.0000).

•

 The intercept is 

7.7986

, which is the expected value of the outcome

(

loss

) when all predictors equal 0 (whether that is realistic or not).

•

The coefficient for 

hours

 is -9.3757 and is the effect of 

hours

 when

effort

 equals 0 (even though that is not a value in the dataset).

•

The coefficient for 

effort

 is -0.0803 and is the effect of 

effort

 when

hours

 equals 0 (even though that is not a value in the dataset).

•

The coefficients for 

hours

 and 

effort

 can be called simple slopes

(similar to simple effects for categorical predictors). (page 302)

Interpretation

•

The coefficient of the interaction term 

int_1

 is 0.3933 and shows how

much the difference in 

loss

 between two cases that differ by one unit

on 

hours

 changes as 

effort

 changes by one unit. (page 294)

Getting Johnson-Neyman significance region

dataset activate exercise.

process y = loss /x = hours /w = effort /model = 1 /plot = 1 /jn = 1.

PROCESS output

Moderator value(s) defining Johnson-Neyman significance region(s):

      Value      % below    % above

    28.5494    41.6667    58.3333

Using moments instead of percentiles

dataset activate exercise.

means var = hours effort.

process y = loss /x = hours /w = effort /model = 1 /plot = 1 /moments = 1.

PROCESS output

 Focal predict: hours    (X)

          Mod var: effort   (W)

Conditional effects of the focal predictor at values of the moderator(s):

      effort         Effect           se              t                p            LLCI          ULCI

    24.5165       .2678     1.3498       .1984      .8428    -2.3813     2.9169

    29.6592     2.2907       .9151     2.5032      .0125        .4947     4.0866

    34.8020     4.3136     1.3087     3.2962      .0010      1.7452     6.8819

PROCESS output

DATA LIST FREE/

   hours      effort     loss       .

BEGIN DATA.

     1.5079    24.5165     6.2343

     2.0024    24.5165     6.3668

     2.4969    24.5165     6.4992

     1.5079    29.6592     8.8717

     2.0024    29.6592    10.0046

     2.4969    29.6592    11.1374

     1.5079    34.8020    11.5091

     2.0024    34.8020    13.6424

     2.4969    34.8020    15.7756

END DATA.

GRAPH/SCATTERPLOT=

 hours    WITH     loss     BY       effort   .

How are the three values calculated?

means var = effort.

29.6592 – 5.14276 = 24.51644

29.6592 + 5.14276 = 34.80196

User-provided values

dataset activate exercise.

process y = loss /x = hours /w = effort /model = 1 /plot = 1 /wmodval = 15,40.

PROCESS output

 Focal predict: hours    (X)

          Mod var: effort   (W)

Conditional effects of the focal predictor at values of the moderator(s):

      effort        Effect           se               t                p           LLCI           ULCI

    15.0000    -3.4755     2.9238    -1.1887      .2349    -9.2137     2.2627

    40.0000     6.3582     2.1182     3.0016      .0028     2.2009    10.5155

PROCESS output

DATA LIST FREE/

   hours      effort     loss       .

BEGIN DATA.

     1.5165    15.0000     1.3241

     2.0051    15.0000     -.3743

     2.4859    15.0000    -2.0451

     1.5165    40.0000    14.2295

     2.0051    40.0000    17.3366

     2.4859    40.0000    20.3932

END DATA.

GRAPH/SCATTERPLOT=

 hours    WITH     loss     BY       effort   .

Graph of interaction (same as above)

GPL syntax to make the same graph

GGRAPH

  /GRAPHDATASET NAME="GraphDataset" VARIABLES= hours loss effort

  /GRAPHSPEC SOURCE=INLINE.

BEGIN GPL

SOURCE: s=userSource( id( "GraphDataset" ) )

DATA: loss=col( source(s), name( "loss" ) )

DATA: hours=col( source(s), name( "hours" ), unit.category() )

DATA: effort = col(source(s), name("effort"), unit.category())

GUIDE: axis( dim( 1 ), label( "hours" ) )

GUIDE: axis( dim( 2 ), label( "effort" ) )

ELEMENT: point( position( hours * loss )) , shape(effort))

ELEMENT: line(position(smooth.linear(hours * loss)), color(effort))

END GPL.

GPL graph of interaction

Two two-way interactions

AKA additive multiple moderation

Conceptual diagram

W

W

X

X

Y

Y

Z

Z

Statistical model

X

X

W

W

XW

XW

Y

Y

Z

Z

XZ

XZ

SPSS GLM syntax for two two-way interactions

dataset activate exercise.

glm loss with hours effort female

    /design = hours effort female hours*effort hours*female

    /print  = parameter.

SPSS GLM output

SPSS GLM output

PROCESS syntax for two two-way interactions

dataset activate exercise.

process y = loss /x = hours /w = effort /z = female /model = 2 /intprobe

= 1 /plot = 1.

Notice that model = 2!

PROCESS output

Model  : 2

    Y  : loss

    X  : hours

    W  : effort

    Z  : female

Sample

Size:  900

PROCESS output

OUTCOME VARIABLE:

 loss

Model Summary

       R             R-sq        MSE             F                df1          df2                 p

      .2827      .0799      183.9470    15.5345     5.0000   894.0000      .0000

Model

              coeff               se                t                p          LLCI            ULCI

constant    10.6681    11.8142      .9030      .3668   -12.5186    33.8549

hours        -10.8798     5.7817    -1.8818      .0602   -22.2271        .4674

effort            -.0956      .3851        -.2483      .8039       -.8514        .6601

Int_1              .4031      .1878        2.1466      .0321        .0345        .7717

female        -4.7227     3.7784     -1.2499      .2117   -12.1383      2.6929

Int_2            2.3918     1.8327      1.3051      .1922    -1.2051       5.9886

Product terms key:

 Int_1    :        hours    x        effort

 Int_2    :        hours    x        female

PROCESS output

Test(s) of highest order unconditional interaction(s):

               R2-chng       F              df1         df2                  p

X*W       .0047     4.6077     1.0000   894.0000      .0321

X*Z      

 .0018     1.7032     1.0000   894.0000      .1922

BOTH      .0063     3.0538     2.0000   894.0000      .0477

PROCESS output

 Focal predict: hours    (X)

          Mod var: effort   (W)

          Mod var: female   (Z)

Conditional effects of the focal predictor at values of the moderator(s):

     effort         female     Effect          se              t                 p            LLCI          ULCI

    24.5391      .0000      -.9879     1.6589     -.5955        .5516    -4.2438     2.2679

    24.5391     1.0000     1.4038     1.6004      .8772       .3806    -1.7371     4.5448

    29.6340      .0000      1.0659     1.3067      .8157       .4149    -1.4986     3.6304

    29.6340     1.0000     3.4577     1.2843     2.6923      .0072       .9371     5.9782

    34.7141      .0000      3.1137     1.5776     1.9737      .0487       .0175     6.2099

    34.7141     1.0000     5.5055     1.6010     3.4388      .0006     2.3634     8.6476

PROCESS output

DATA LIST FREE/

   hours      effort     female     loss       .

BEGIN DATA.

     1.5165    24.5391      .0000     6.8235

     2.0051    24.5391      .0000     6.3407

     2.4859    24.5391      .0000     5.8658

     1.5165    24.5391     1.0000     5.7279

     2.0051    24.5391     1.0000     6.4139

     2.4859    24.5391     1.0000     7.0888

     1.5165    29.6340      .0000     9.4508

     2.0051    29.6340      .0000     9.9717

     2.4859    29.6340      .0000    10.4841

     1.5165    29.6340     1.0000     8.3552

     2.0051    29.6340     1.0000    10.0449

     2.4859    29.6340     1.0000    11.7071

     1.5165    34.7141      .0000    12.0705

     2.0051    34.7141      .0000    13.5921

     2.4859    34.7141      .0000    15.0889

     1.5165    34.7141     1.0000    10.9748

     2.0051    34.7141     1.0000    13.6653

     2.4859    34.7141     1.0000    16.3119

END DATA.

PROCESS output

GRAPH/SCATTERPLOT=

 hours    WITH     loss     BY       effort   /PANEL   ROWVAR=  female   .

PROCESS output

Level of confidence for all confidence intervals in output:

  95.0000

W values in conditional tables are the 16th, 50th, and 84th percentiles.

Graph of interaction

Interpretation

•

The coefficient for 

hours

, -10.8798, estimates the conditional effect of

hours

 on 

loss

 when both 

effort

 and 

female

 equal 0.

•

The coefficient for 

effort

, -0.0956, estimates the conditional effect of 

effort

on 

loss

 when 

hours

 equals 0 while holding 

female

 constant.

•

The coefficient for 

female

, -4.7227, estimates the conditional effect of

female

 on 

loss

 when 

hours

 equals 0 while holding 

effort

 constant.

•

The coefficient for the 

hours

 by 

effort

 interaction (int_1), 0.4031,

quantifies how much the conditional effect of 

hours

 on 

loss

 changes as

effort

 changes by one unit, holding 

female

 constant.

•

The coefficient for the 

hours

 by 

female

 interaction (int_2), 2.3918,

estimates the how much the conditional effect of 

hours

 on 

loss

 changes as

female

 changes by one unit, holding 

effort

 constant. (page 339)

Three-way interaction

AKA moderated moderation

Conceptual diagram

W

W

X

X

Y

Y

Z

Z

Statistical model

X

X

W

W

Z

Z

Y

Y

WX

WX

XZ

XZ

WZ

WZ

XWZ

XWZ

Try it yourself

•

Write the SPSS GLM syntax for a model with a three-way interaction.

•

Why might the output not match the PROCESS output for some

coefficients?

PROCESS syntax for three-way interaction

dataset activate exercise.

process y = loss /x = hours /w = effort /z = female /model = 3 /plot = 1.

PROCESS output

Model  : 3

    Y  : loss

    X  : hours

    W  : effort

    Z  : female

Sample

Size:  900

PROCESS output

OUTCOME VARIABLE:

 loss

Model Summary

          R           R-sq            MSE              F               df1          df2                 p

      .2841      .0807      184.2046    11.1877     7.0000   892.0000      .0000

Model

                     coeff             se                t               p             LLCI             ULCI

constant    11.2045    16.5171      .6784       .4977     -21.2123     43.6214

hours        -12.2037      8.0012    -1.5252      .1276     -27.9072       3.4997

effort            -.1105         .5458     -.2025       .8395       -1.1817         .9606

Int_1              .4460         .2633     1.6939      .0906         -.0708         .9627

female       -6.5873     23.2663     -.2831       .7771    -52.2504      39.0759

Int_2            5.4813     11.3637      .4824       .6297    -16.8214      27.7840

Int_3              .0605         .7715      .0784        .9375     -1.4536         1.5747

Int_4             -.1030         .3764     -.2736       .7845       -.8417           .6357

PROCESS output

Product terms key:

 Int_1    :        hours    x        effort

 Int_2    :        hours    x        female

 Int_3    :        effort   x        female

 Int_4    :        hours    x        effort     x      female

Test(s) of highest order unconditional interaction(s):

                R2-chng        F             df1           df2                p

X*W*Z      .0001      .0748     1.0000   892.0000      .7845

PROCESS output

DATA LIST FREE/

   hours      effort     female     loss       .

BEGIN DATA.

     1.5165    24.5391      .0000     6.5816

     2.0051    24.5391      .0000     5.9660

     2.4859    24.5391      .0000     5.3604

     1.5165    24.5391     1.0000     5.9598

     2.0051    24.5391     1.0000     6.7880

     2.4859    24.5391     1.0000     7.6028

     1.5165    29.6340      .0000     9.4641

     2.0051    29.6340      .0000     9.9590

     2.4859    29.6340      .0000    10.4457

     1.5165    29.6340     1.0000     8.3551

     2.0051    29.6340     1.0000    10.0374

     2.4859    29.6340     1.0000    11.6924

     1.5165    34.7141      .0000    12.3383

     2.0051    34.7141      .0000    13.9403

     2.4859    34.7141      .0000    15.5162

     1.5165    34.7141     1.0000    10.7434

     2.0051    34.7141     1.0000    13.2773

     2.4859    34.7141     1.0000    15.7699

END DATA.

PROCESS output

GRAPH/SCATTERPLOT=

 hours    WITH     loss     BY       effort   /PANEL   ROWVAR=  female   .

Graph of three-way interaction

Interpretation

•

“Regression coefficients for products involving X in these models

quantify the rate of change of X’s effect as one moderator changes

when another moderator is held fixed (additive multiple moderation)

or as another moderator varies (moderated moderation).” (page 359)

Try it yourself

•

Rewrite the PROCESS syntax so that w = female and z = effort.

•

Run the resulting graph code.

•

Do you like this graph better?

Adding covariates

dataset activate hsbm.

process y = opinion /x = detail /w = age /cov = ccovar bcovar /model = 1

/plot = 1.

Model  : 1

    Y  : opinion

    X  : detail

    W  : age

Covariates:

 ccovar   bcovar

Sample

Size:  200

PROCESS output

OUTCOME VARIABLE:

 opinion

Model Summary

          R           R-sq        MSE              F              df1            df2               p

      .6907      .4770    61.8295    35.3917     5.0000   194.0000      .0000

Model

                      coeff           se                 t               p              LLCI          ULCI

constant    10.3742    17.7519      .5844      .5596      -24.6374    45.3857

detail              .3021      .3596        .8401      .4019          -.4072     1.0115

age                  .3148      .3280        .9597      .3384           -.3322      .9618

Int_1               .0013      .0065        .1924      .8477           -.0116      .0141

ccovar             .1185      .0872       1.3590     .1757           -.0535      .2906

bcovar            -.2354     1.2110     -.1943      .8461          -2.6238     2.1531

Product terms key:

 Int_1    :        detail   x        age

Heteroskedastic SEs

dataset activate hsbm.

process y = opinion /x = detail /w = age /hc = 4 /model = 1 /plot = 1.

Heteroskedastic SEs output

OUTCOME VARIABLE:

 opinion

Model Summary

          R           R-sq        MSE          

F(HC4)

        df1            df2                p

      .6868      .4716    61.8301    69.9503     3.0000   196.0000      .0000

Model

                    coeff           

se(HC4)

        t              p           LLCI           ULCI

constant    15.2578     17.4022      .8768      .3817   -19.0619    49.5775

detail             .2853          .3504      .8141      .4166     -.4058      .9763

age                 .2866          .3242      .8841      .3777     -.3528      .9260

Int_1              .0025          .0062      .4084      .6834     -.0097      .0148

Product terms key:

 Int_1    :        detail   x        age

Test(s) of highest order unconditional interaction(s):

            R2-chng     

F(HC4)

      df1           df2                p

X*W      .0004      .1668     1.0000   196.0000      .6834

Changing number of decimal places in output

dataset activate hsbm.

process y = opinion /x = detail /w = age /decimals = f10.2 /model = 1

/plot = 1.

All values to two decimal places

Model Summary

          R         R-sq    MSE        F               df1        df2              p

        .69        .47      61.83      58.32       3.00     196.00        .00

Model

                     coeff        se              t            p         LLCI       ULCI

constant      15.26      17.39        .88        .38     -19.04      49.56

detail                .29          .36        .79        .43       -.42        .99

age                    .29          .33        .88        .38       -.36        .93

Int_1                 .00          .01        .39        .69       -.01        .02

Product terms key:

 Int_1    :        detail   x        age

Test(s) of highest order unconditional interaction(s):

            R2-chng     F         df1        df2              p

X*W        .00        .15       1.00     196.00        .69

All values to two decimal places

DATA LIST FREE/

   detail     age        opinion    .

BEGIN DATA.

      42.00      41.00      43.35

      50.00      41.00      46.46

      63.00      41.00      51.52

      42.00      54.00      48.46

      50.00      54.00      51.83

      63.00      54.00      57.32

      42.00      62.00      51.60

      50.00      62.00      55.14

      63.00      62.00      60.88

END DATA.

GRAPH/SCATTERPLOT=

 detail   WITH     opinion  BY       age      .

Try it yourself

•

What is the difference between reporting coefficients and

interpreting coefficients?

•

Do you need to interpret all of the coefficients in your regression

output?

•

Do you need to report all of the coefficients in your regression

output, or only those that you interpret?

Useful pages in Appendix A

•

Page 581:  the syntax diagram

•

Page 621:  the diagrams of the models

•

Page 594:  codings for multicategorical variables X, W and Z

•

Page 598:  visualizing interactions

•

Page 599:  probing interactions

•

Page 601:  comparing conditional effects

•

Page 609:  long variable names

•

Page 611:  options not available in the PROCESS dialog box

•

Page 618:  important notes that may answer your questions about how 

          PROCESS works