MLmed User Guide 5 17

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MLMED

User Guide

Nicholas J. Rockwood

The Ohio State University

rockwood.19@osu.edu

Beta Version

May, 2017

MLmed is a computational macro for SPSS that simpliﬁes the ﬁt-

ting of multilevel mediation and moderated mediation models, including

models containing more than one mediator. After the model speciﬁca-

tion, the macro automatically performs all of the tedious data manage-

ment necessary prior to ﬁtting the model. This includes within-group

centering of lower-level predictor variables, creating new variables con-

taining the group means of lower-level predictor variables, and stacking

the data as outlined in Bauer, Preacher, and Gil (2006) and their supple-

mentary material to allow for the simultaneous estimation of all param-

eters in the model. The output is conveniently separated by equation,

which includes a further separation of between-group and within-group

eﬀects. Further, indirect eﬀects, including Monte Carlo conﬁdence in-

tervals around these eﬀects, are automatically provided. The index of

moderated mediation (Hayes, 2015) is also provided for models involv-

ing level-2 moderators of the indirect eﬀect(s).

Contents

1 Scope of MLmed 3

2 System Requirements 3

2.1 Note for using SPSS Version 21 . . . . . . . . . . . . . . . . . 3

2.2 OutputLanguage......................... 4

3 Preparation for Use 4

4 Model Syntax 4

4.1 Adding Fixed Eﬀects . . . . . . . . . . . . . . . . . . . . . . . 6

4.1.1 Mediators ......................... 6

4.1.2 Level-1 Covariates . . . . . . . . . . . . . . . . . . . . 6

4.1.3 Level-2 Covariates . . . . . . . . . . . . . . . . . . . . 6

4.1.4 Level-2 Moderators . . . . . . . . . . . . . . . . . . . . 6

4.2 Removing Fixed Eﬀects . . . . . . . . . . . . . . . . . . . . . 7

4.2.1 Between-group Eﬀects . . . . . . . . . . . . . . . . . . 7

4.2.2 Within-group Eﬀect of X . . . . . . . . . . . . . . . . . 8

4.3 Specifying Random Eﬀects . . . . . . . . . . . . . . . . . . . . 8

4.3.1 Random Intercepts . . . . . . . . . . . . . . . . . . . . 8

4.3.2 RandomSlopes ...................... 9

4.4 Covariance Matrices . . . . . . . . . . . . . . . . . . . . . . . 9

4.4.1 Residual Covariance Matrix . . . . . . . . . . . . . . . 9

4.4.2 Random Eﬀect Covariance Matrix . . . . . . . . . . . . 9

4.5 Estimation............................. 10

4.6 Other Speciﬁcations . . . . . . . . . . . . . . . . . . . . . . . . 10

5 Example Syntax 10

5.1 RandomSlopes .......................... 11

5.2 Parallel Mediators with Covariates . . . . . . . . . . . . . . . 11

5.3 Moderated Mediation . . . . . . . . . . . . . . . . . . . . . . . 12

5.4 2-1-1Design............................ 12

5.5 1-1-1 Design with No Between Eﬀects . . . . . . . . . . . . . . 13

6 Output 13

6.1 Errors ............................... 13

6.2 Model Fit Statistics . . . . . . . . . . . . . . . . . . . . . . . . 14

6.3 FixedEﬀects ........................... 14

6.4 RandomEﬀects.......................... 14

6.5 Index of Moderated Mediation . . . . . . . . . . . . . . . . . . 15

6.6 IndirectEﬀect(s) ......................... 15

References 15

1 Scope of MLmed

Currently, MLmed is fairly limited in terms of available models relative to

other macros available for mediation, moderation, and conditional process

models, such as PROCESS (Hayes, 2013). MLmed is, in fact, a work in

progress that will be expanded upon as time permits. Generally, these

expansions will be made following research and user recommendations.

In its current form, MLmed can accommodate up to three continuous, par-

allel mediators and one continuous dependent variable. Up to three level-1

and three level-2 covariates can be included. Finally, one level-2 moderator

of the apath (X→M) and one level-2 moderator of the bpath (M→Y)

can be included. The same variable may moderate both paths. In models

containing more than one mediator, only the aand bpaths for the ﬁrst me-

diator may be moderated. Further, the direct eﬀect for any model cannot

be moderated. For those familiar with PROCESS (Hayes, 2013), MLmed

can handle multilevel models similar to Models 4, 7, 14, 21, and 58. A

special multilevel type of Model 74 can also be ﬁt.

Within-group and between-group indirect eﬀects can be estimated when X,

M, and Yall have variability at the within-group and between-group levels.

MLmed estimates within-group eﬀects by within-group centering variables

prior to the analysis, and between-group eﬀects are estimated using group

means. The details of this approach can be found in Zhang, Zyphur, and

Preacher (2009).

In connection to the multilevel mediation literature, MLmed can handle 1-

1-1 and 2-1-1 data designs, where the three numbers refer to the lowest

level in which X,M, and Yvary.

2 System Requirements

MLmed is compatible with Windows and Mac Operating Systems for SPSS

Version 21 and higher. For the most user-friendly output, it is recommended

that SPSS Version 22 or higher is used.

2.1 Note for using SPSS Version 21

MLmed contains syntax to remove unnecessary additional output provided

by the use of the MIXED function in SPSS. However, this syntax is not

recognized by SPSS versions older than Version 22. As a result, the ad-

ditional output will not be removed and the output will also contain the

following error code in numerous places:

>Error # 1. Command name: OUTPUT

>The first word in the line is not recognized as an SPSS

Statistics command.

>Execution of this command stops.

This error is simply due to attempts to modify the output display, and is

not an indication of error in the output content. Consequently, users should

ignore the warnings and additional output that is presented and instead

focus on the output discussed in this manual and subsequent publications

and tutorials.

2.2 Output Language

Unfortunately, the use of MLmed when the SPSS Output Language is spec-

iﬁed as anything other than English will result in errors. The output lan-

guage can be changed to English using the Output Language drop-down

menu under the Language header found through Edit →Options....

3 Preparation for Use

Before using MLmed, the syntax ﬁle containing the code necessary to deﬁne

the macro (MLmed.sps), must be opened and executed without modiﬁca-

tion. The ﬁle can then be closed, and MLmed can be operated using a new

syntax ﬁle. Note that the macro will remain active only for the duration

of the SPSS session (i.e., until SPSS is closed). The macro will need to be

re-executed at the start of a new session.

4 Model Syntax

Once the macro is activated, it can be called by typing MLmed followed by

the appropriate macro arguments. Each argument, except the ﬁrst, should

begin with a forward slash, and the ﬁnal argument should be followed by a

period. The minimum syntax necessary to run the most basic model is:

MLmed data = DataSet1

/x = Xvar

/m1 = Mvar

/y = Yvar

/cluster = group

/folder = FilePath.

where the italicized words are replaced with the correct dataset name, vari-

able names, and ﬁle location. The dataset name should be the name that

appears in brackets on the opened dataset window, rather then the saved

.sav ﬁle name. By default, the ﬁrst dataset opened in a new SPSS session

is named DataSet1 and MLmed defaults to this name. To be safe, specify

the correct dataset name, even if it is the default. The x,m1, and yar-

guments should be the names of the variables in the dataset corresponding

to X,M, and Y. The cluster argument should be a variable that labels

which level-2 unit each row in the dataset belongs to. Finally, the folder

argument should be a ﬁle path on the user’s computer. This does not have

to be the location of the dataset, syntax ﬁle, or any other speciﬁc ﬁle, but

must be a correct folder location on the computer. Note that ﬁle paths on

a Windows OS will use a backslash between folders, while a Mac OS will

use a forward slash (see Section 5 for examples). The macro arguments do

not have to be in any speciﬁc order, other than the folder speciﬁcation

being last.

This minimum syntax will ﬁt a model where Xvar is the independent

variable, Mvar is the mediator, and Yvar is the dependent variable. The

macro automatically group-mean centers Xand uses the group means as

a level-2 predictor of M. Further, group-mean centered Xand Mare

used as level-1 predictors of Yand the group means of Xand Mare

used as level-2 predictors. All intercept terms are random. By default,

all slope terms (described in this section and later sections) are ﬁxed and

the random eﬀect covariance matrix is diagonal, where variances are freely

estimated and covariances are constrained to zero. These defaults are useful

for increasing the likelihood of convergence. Macro arguments that can

change these speciﬁcations are described in a later section.

4.1 Adding Fixed Eﬀects

The basic syntax can be expanded to ﬁt models that include additional ﬁxed

eﬀects that result from adding mediators, covariates, and moderators.

4.1.1 Mediators

Up to two additional mediators can be speciﬁed by including the arguments

m2 and m3 with the variable name following. Each mediator included will

be group-mean centered prior to the analysis. The group means will also

be included as predictors to estimate between-group eﬀects.

4.1.2 Level-1 Covariates

Up to three level-1 covariates can be included by using the cov1,cov2,

and cov3 arguments, with the appropriate variable names following. As

with other level-1 variables, the covariates are automatically group mean

centered to disentangle between-group and within-group eﬀects.

4.1.3 Level-2 Covariates

Up to three level-2 covariates can be included by using the L2cov1,L2cov2,

and L2cov3 arguments, with the name of the covariates following. The

user should manually center level-2 covariates prior to using MLmed if de-

sired.

4.1.4 Level-2 Moderators

One level-2 moderator can be speciﬁed for the apath, and one level-2 mod-

erator can be speciﬁed for the bpath. These are speciﬁed using the modM

and modY arguments, respectively, where the letters Mand Ycorrespond to

the dependent variable for the equation in which the moderator is included

in. The user should NOT include the level-2 moderator as a level-2 covari-

ate, as MLmed will do this automatically. It should also be noted that the

variable is included as a moderator only for the ﬁrst mediator listed (the

one speciﬁed by m1).

By default, the moderation of both the between-group and within-group

eﬀects are tested for each moderator included. The same moderator can be

speciﬁed for both paths to allow for the testing of a quadratic moderation

eﬀect. The user can also specify a speciﬁc value to center each modera-

tor around using the modMcent and modYcent arguments, respectively.

Any eﬀect that is moderated will be conditional on the value in which the

moderator is centered around (by default, the value is 0).

4.2 Removing Fixed Eﬀects

Some of the eﬀects automatically included by MLmed may be omitted from

the model. These include a number of between-group eﬀects, and also the

within-group eﬀect of X.

4.2.1 Between-group Eﬀects

The general format for removing a between group eﬀect is by listing the

argument to specify the original variable followed by a Band setting this

new argument equal to zero. That is, it can be thought of as specify-

ing that between-group eﬀect to be omitted. For example, removing the

between-group eﬀect of xcan be speciﬁed using the argument xB = 0.

The between-group eﬀect of cov1 can be omitted using cov1B = 0. Sim-

ilarly, the between-eﬀects of the Mand/or Ymoderators can be speciﬁed

using modMB = 0 and ModYB = 0, respectively.

There is, however, a slight deviation from this format for removing the

between-group eﬀect(s) of the mediator(s). Rather than the between-group

eﬀect of each mediator being speciﬁed with its own argument, the between-

group eﬀect of all mediators can be speciﬁed using mB, which should be a

list of zeros and ones equal in length to the number of mediators where a

1 denotes that the between-group eﬀect of that particular mediator should

be estimated and a 0 denotes it should be omitted. For example, a model

including three mediators where the between-group eﬀect of mediators 1

and 3 on Yis estimated, but the eﬀect of mediator 2 on Yis omitted can

be speciﬁed using mB = 101.

There are two main reasons one may wish to omit a between-group eﬀect.

The ﬁrst occurs if there is no actual between-group variability on a given

variable. In this scenario, the group-mean for the variable will be the same

for each group, making the vector of group means redundant. Consequently,

the model cannot be estimated without this eﬀect omitted. The second

reason is simply for parsimony, as the removal of the eﬀect can simplify

the model. This is particularly true with the removal of the between-group

moderator, given that including the moderator makes the indirect eﬀect

conditional. It should be noted that if the between-group eﬀect of Xor

one of the mediators is not estimated, the between-group indirect eﬀect

involving that parameter is also not calculated.

4.2.2 Within-group Eﬀect of X

The within-group eﬀect of Xcan also be omitted using the argument xW =

0. Of course, no within-group indirect eﬀects will then be estimated. The

ability to omit the within-group eﬀect of Xexpands MLmed to be able to

estimate 2-1-1 multilevel mediation models, as the 2-1-1 model can be seen

as a special case of the 1-1-1 model with no within-group variability on X.

4.3 Specifying Random Eﬀects

Any intercept and/or within-group slope included in the model can be

speciﬁed as randomly varying across groups.

4.3.1 Random Intercepts

By default, all intercepts included in the model are speciﬁed as random.

Because nonconvergence may be an issue if the variance of a random eﬀect

nears zero, the user can specify any intercept as ﬁxed. For the Yintercept,

this is accomplished using randYint = 0, indicating that a random term

for the Yintercept should be omitted. For M, the argument to omit a

random intercept is randMint, though the exact speciﬁcation depends on

the number of mediators in the model. A list of zeros and ones that is the

length of the number of mediators should be included, where a zero omits

the random eﬀect and a one estimates it. For example, randMint = 011

should be speciﬁed to omit the random intercept for the ﬁrst mediator in

a three mediator model.

4.3.2 Random Slopes

Random slopes can be speciﬁed using similar syntax as random intercepts.

To specify the eﬀect of Xto be random, the argument randx is used,

which should be a list of binaries of length k+ 1 where kis the number of

mediators in the model. The ﬁrst binary refers to the eﬀect of Xon Y(the

c0path), the second refers to the eﬀect of Xon M1, the third refers to the

eﬀect of Xon M2, and so forth. A 1 corresponds to a random eﬀect, while a

0 corresponds to a ﬁxed eﬀect. Random eﬀects of the mediator(s) on Yare

speciﬁed using randm which should be a list of binaries of length k, where

the ﬁrst refers to the eﬀect of the ﬁrst mediator on Y, the second refers

to the eﬀect of the second mediator on Yand so forth. Random eﬀects of

level-1 covariates are speciﬁed using randc1,randc2, and randc3. The

format of these arguments follow that of randx.

4.4 Covariance Matrices

The residual covariance matrix and the covariance matrix of the random

eﬀects can be modiﬁed.

4.4.1 Residual Covariance Matrix

The residual covaraince matrix is speciﬁed as diagonal (DIAG) by default,

where the residual variance of each equation is freely estimated and the

covariance between the residuals of each equation are constrained to zero.

The residual covariance matrix can be speciﬁed as unconstrained (where

all variances and covariances are freely estimated) using the argument

rescovmat = UN.

4.4.2 Random Eﬀect Covariance Matrix

By default, the random eﬀect covariance matrix is speciﬁed as diagonal,

where all variances are freely estimated and the covariances are constrained

to zero. However, some or all of the random eﬀects can be permitted to

covary. If there is more than one random slope, their covaraince(s) can be

freely estimated by including the command covmat = UN. To estimated

the covariance between random slopes and the Yintercept, the command

ycov = 1 can be included (if covmat = UN). If more than one mediator

is in the model, the covariance between the random intercepts for the me-

diators can be estimated using mcovmat = UN. The covariance between

the Mand Yintercepts can be included in the model using indint = 0.

If there are random slopes in the model, covmat = UN,ycov = 1, and

indint = 0, then the whole random eﬀect covariance matrix is unstruc-

tured, where all variances and covariances are freely estimated.

4.5 Estimation

The default estimator for MLmed is Restricted Maximum Likelihood (REML).

Users may instead estimate the model using Full Maximum Likelihood by

including the argument est = ML. The user may also provide a num-

ber of speciﬁcations that inﬂuence the estimation. These speciﬁcations

include iters (maximum number of iterations), mxstep (maximum step-

halving), and scoring (number of iterations in which the Fisher scoring

algorithm is used). Further details of these can be found in the SPSS users

manual under the section for MIXED.

4.6 Other Speciﬁcations

The user may specify the conﬁdence level used for inferences provided in the

output using the conf argument, which should include a number between

0 and 100 which corresponds to the percentage of conﬁdence. By default,

this value is 95. The number of Monte Carlo samples used can be changed

using samples, which defaults to 10,000. Lastly, when the model fails to

converge the estimates of the parameters is omitted from the output. The

user may override this by specifying eor = 1, which is short for Error

Override. This command can be useful for assessing issues in convergence

by identifying which parameters may be causing the diﬃculties.

5 Example Syntax

This section contains example models to demonstrate the use of some the

syntax arguments described previously. The models presented here are not

exhaustive. The arguments from each of the following example models can

be mixed and matched to correspond to the user’s desired model.

5.1 Random Slopes

MLmed data = DataSet1

/x = Xvar

/randx = 11

/m1 = Mvar

/randm = 1

/y = Yvar

/covmat = UN

/cluster = group

/folder = /Users/username/Desktop/.

Here, randx = 11 speciﬁes that the within-group eﬀects of Xon Yand M

randomly vary across upper-level units. The randm = 1 speciﬁes that the

within-group eﬀect of Mon Yis also random. The covariance between these

random slopes is estimated using covmat = UN. Finally, the folder

argument is an example of a correct folder on a Mac.

5.2 Parallel Mediators with Covariates

MLmed data = DataSet1

/x = Xvar

/randx = 010

/cov1 = Covvar

/L2cov1 = L2Covvar

/m1 = Mvar1

/m2 = Mvar2

/randm = 10

/mcovmat = UN

/y = Yvar

/cluster = group

/folder = C:\Users\rockwood.19\Desktop\.

This model is a parallel mediator model with mediators Mvar1 and Mvar2,

level-1 covariate Covvar, and level-2 covariate L2Covvar. The within-

group eﬀects of Xon Y,M1, and M2are ﬁxed, random, and ﬁxed, respec-

tively, as deﬁned by randx = 010. Further, the within-group eﬀect of

M1on Yis random, while the within-group eﬀect of M2on Yis ﬁxed, as

speciﬁed by randm = 10. Estimation of the covariance between the ran-

dom intercepts for the M1and M2equations is requested using mcovmat

= UN.

5.3 Moderated Mediation

MLmed data = DataSet1

/x = Xvar

/randx = 01

/m1 = Mvar

/modM = Modvar

/modMB = 0

/modMcent = 2.3

/y = Yvar

/cluster = group

/folder = /Users/username/Desktop/.

This is a moderated mediation model in which the apath is moderated

by Modvar. By default, the moderation of both the within-group and

between-group eﬀects is estimated. However, the inclusion of modMB =

0omits the between-group moderation. The moderator is also centered

around 2.3 prior to the analysis using modMcent = 2.3. The residual

variance of the within-group apath is estimated using randx = 01. That

is, the within-group eﬀect of Xon Mrandomly varies after controlling for

Modvar.

5.4 2-1-1 Design

MLmed data = DataSet1

/x = Xvar

/xW = 0

/m1 = Mvar

/y = Yvar

/cluster = group

/folder = /Users/username/Desktop/.

This is a standard 2-1-1 design with only random intercepts. It follows

the same sytnax as the basic 1-1-1 design with the exception that the

argument xW = 0 is included to omit the estimation of the within-group

eﬀect of Xwhich, by deﬁnition, does not exist (since Xhas no within-group

variability).

5.5 1-1-1 Design with No Between Eﬀects

MLmed data = DataSet1

/x = Xvar

/xB = 0

/m1 = Mvar

/mB = 0

/y = Yvar

/cluster = group

/folder = /Users/username/Desktop/.

This is the standard 1-1-1 design without the estimation of between-group

eﬀects. The between-group eﬀects of Xare omitted using xB = 0, and

the between-group eﬀect of Mis omitted using mB = 0. Note that Xand

Mare still within-group centered prior to the analysis.

6 Output

The MLmed macro provides a very detailed output including individual

parameter estimates, and the estimated indirect eﬀects. In addition, the

index of moderated mediation is included if a moderator is speciﬁed. This

section provides an overview on each of the output tables provided.

6.1 Errors

If there are any errors when estimating the model, the estimated parameters

are disabled from the output (unless this is overridden). Instead, the user is

provided with the number of ﬁxed eﬀect and random eﬀect parameters that

could not be estimated, as well as a code labeling the speciﬁc parameters,

where a 1 indicates the parameter could not be estimated. The user can

use this information to respecify the model.

6.2 Model Fit Statistics

If the model converges, various statistics are provided, such as the sample

size and number of model parameters, as well as several model ﬁt statis-

tics, including -2 times the Log Likelihood (-2LL), Akaike’s Information

Criterion (AIC), Hurvich and Tsai’s Criterion (AICC), Bozdogan’s Crite-

rion (CAIC), and Schwarz’s Bayesian Criterion (BIC). The ﬁt statistics can

be useful when comparing models.

6.3 Fixed Eﬀects

After the model ﬁt statistics, the ﬁxed eﬀect estimates are provided. These

estimates are grouped by each outcome variable, starting with the medi-

ator(s) and ending with Y. Within each section containing each outcome

variable, the eﬀects are broken up by within-group and between-group ef-

fects. If no covariates are included in the model and the between-group

eﬀect of Xis disabled, there will not be any between-group eﬀects in each

of the mediators’ sections. If any moderators are included, the interaction

terms are labeled using int, and the Interaction Codes section contains

information on what each interaction term represents.

6.4 Random Eﬀects

If the level-1 residual covariance matrix is speciﬁed as diagonal, the esti-

mates are displayed in the Level-1 Residual Estimates section. If the matrix

is speciﬁed as unstructured, the eﬀects are labeled with a number system

where the eﬀect is a variance parameter if the two numbers in parentheses

are the same, and a covariance parameter if the two numbers diﬀer. The

numbers correspond to the key provided below the table.

If the random eﬀect covariance matrix is speciﬁed as diagonal (the default),

the Random Eﬀects section of the output will contain the estimated vari-

ance of each random eﬀect, as well as the relevant test statistics for that

eﬀect. If the covariance matrix is speciﬁed as unstructured, the Random Ef-

fect Estimates table will contained each estimated variance and covariance

parameter, as well as the relevant test statistics for each of these param-

eters. These eﬀects use the same number system as the Level-1 Residual

Estimates section. A table containing the number key for each eﬀect is

also included. Finally, the estimated covariance and correlation matrices

are provided.

6.5 Index of Moderated Mediation

If any moderators are included in the model, an Index of Moderated Medi-

ation section follows the Random Eﬀects section. This section includes the

index of moderated mediation for each interaction term as well as a Monte

Carlo conﬁdence interval. If the same variable is speciﬁed as a moderator

for both aand b, the linear and quadratic terms are included. Further, this

section is broken up by within-group and between-group eﬀects.

6.6 Indirect Eﬀect(s)

The ﬁnal section included in the output contains the indirect eﬀect(s). If

there are any moderators in the model, a code is provided which states what

value of the moderator(s) the indirect eﬀect(s) are conditional on. These

are the values speciﬁed using modMcent and modYcent, which default

to 0. If no moderators are speciﬁed, the indirect eﬀects are unconditional.

The ﬁrst Within- Indirect Eﬀect(s) section displays the estimated average

within-group indirect eﬀect(s), as well as the estimated variability of indi-

rect eﬀects across level-2 units. If neither anor bare random, the variance

of the indirect eﬀect is 0. The next Within- Indirect Eﬀect(s) section con-

tains a normal-theory test on the average within-group indirect eﬀect(s).

A Monte Carlo conﬁdence interval is also provided. Finally, the Between-

Indirect Eﬀect(s) section contains the normal-theory test and Monte Carlo

conﬁdence interval for the between-group indirect eﬀect(s). If xB = 0,

this section is omitted.

If multiple mediators are speciﬁed, a section containing indirect eﬀect con-

trasts follows. Every pairwise combination of indirect eﬀects is tested using

a Monte Carlo conﬁdence interval. This section is broken up by within-

group and between-group eﬀects.

References

Bauer, D. J., Preacher, K. J., & Gil, K. M. (2006). Conceptualizing and

testing random indirect eﬀects and moderated mediation in multi-

level models: new procedures and recommendations. Psychological

Methods,11 (2), 142–163.

Hayes, A. F. (2013). Introduction to mediation, moderation, and conditional

process analysis: A regression-based approach. Guilford Press.

Hayes, A. F. (2015). An index and test of linear moderated mediation.

Multivariate Behavioral Research,50 (1), 1–22.

Zhang, Z., Zyphur, M. J., & Preacher, K. J. (2009). Testing multilevel

mediation using hierarchical linear models problems and solutions.

Organizational Research Methods,12 (4), 695–719.

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