Determine power and sample size for the simple and mediation Actor–Partner Interdependence Model

• Published date: 01 October 2022
• Author: Thomas Ledermann,Myriam Rudaz,Qiong Wu,Ming Cui
• Date: 01 October 2022
• DOI: http://doi.org/10.1111/fare.12644

RESEARCH

Determine power and sample size for the simple and

mediation Actor–Partner Interdependence Model

ThomasLedermann| MyriamRudaz| QiongWu| MingCui

Department of Human Development and

Family Science, Florida State University,

Tallahassee, Florida, USA

Correspondence

Thomas Ledermann, Florida State University,

Department of Human Development and

Family Science, 120 Convocation Way,

Tallahassee, Florida 32306, USA.

Email: tledermann@fsu.edu

Abstract

Objective: We provide details on how relationship

researchers can use Monte Carlo simulation for power esti-

mation and sample size determination for the simple and

the mediation Actor–Partner Interdependence Model

(APIM). In addition to power estimates for specific sample

sizes, we show how the sample size for each effect can be

determined.

Background: Researchers designing a study commonly

want to know what sample size is required to detect a spe-

cific effect or in the case after data collection is completed

what the power is for a specific effect.

Method: The solution we present asks for the correlations

among the variables and allows for the specification of

skewness and kurtosis and the incorporation of missing

data. For the mediation APIM, power is estimated for the

direct effects, indirect effects, and total effects.

Results: The illustrations demonstrate that indistinguishable

members require sample sizes that are about half of the sample

sizes required for distinguishable members and that skewed

data tend to require larger sample sizes. The illustration of the

mediation APIM reveals that it is not uncommon that some

of the simple indirect effects are significant, but none of the

total indirect effects and none of the total effects are.

Conclusion: Monte Carlo simulation provides an easy-to-

use and flexible solution to determine power and sample

sizes for the simple and mediation APIM for distinguish-

able and indistinguishable members.

Implications: Recommendations are made for dyadic studies

with small sample sizes and studies using the mediation APIM.

KEYWORDS

Actor–Partner Interdependence Model, mediation, Monte Carlo

simulation, power analysis

Received: 22 December 2020Revised: 19 April 2021Accepted: 11 August 2021

DOI: 10.1111/fare.12644

© 2022 National Council on Family Relations.

1452 Family Relations. 2022;71:1452–1469.wileyonlinelibrary.com/journal/fare

In designing a study, the determination of how many participants are needed to detect a specific

effect is important because observing more participants than needed is a waste of resources and

inflates the risk for false positive conclusions (i.e., Type 1 error), while studies with too few par-

ticipants have a high risk of drawing false negative conclusions (i.e., Type 2 error). In addition,

adequately powering a study has been crucial for many funding agencies. For a wide variety

of statistical methods, a rough estimate of an appropriate sample size or achieved power can

be obtained by using a standard power analysis software program (see Kelley & Maxwell, 2012,

for a list), such as G*Power (Faul et al., 2007), nQuery (Elashoff, 2007), or PASS 20 (NCSS

Statistical Software, 2020). The current capabilities of these software programs to determine

required sample sizes or the power of specific effects for popular methods developed to study

dyads, such as couples or twins, are limited. Moreover, the assumptions underlying the formula

to calculate power, such as the assumption of normality, are often not met in real data

(e.g., Beaujean, 2014). There are also simple rule of thumb heuristics that researchers sometimes

use, such as 200 cases for Structural Equation Modeling (SEM) analysis, which would imply a

sample size of 400 individuals for a dyadic study.

There is now a wide variety of methods available to dyadic researchers to address a large

range of specific questions (see Kenny et al., 2006; Ledermann & Kenny, 2017). One of the

most popular frameworks is Kenny’s Actor–Partner Interdependence Model (APIM;

Kenny, 1996), which has been designed to assess associations within and between dyad mem-

bers called actor effect and partner effect, respectively. A PsycINFO search revealed that more

than 1000 articles used this model, with more than 200 in 2020.

This article provides researchers with an easy-to-use solution for power estimation for the

simple and mediation APIM for both distinguishable and indistinguishable members using

SEM. The solution provided uses Monte Carlo (MC) simulation in R (R Core Team, 2020) and

requires the product–moment correlations among the variables, which can be taken from previ-

ous research, including meta-analyses, or guessed by the researcher based on similar findings.

For the mediation APIM, power is estimated for each direct effect, the indirect effects, and the

total effects.

THE ACTOR–PARTNER INTERDEPENDENCE MODEL

The APIM consists in its most basic form of a predictor Xand an outcome Y, measured in both

dyad members, which might be mother and child reporting on their attachment and relationship

quality. These two variables can vary both within and between members and are known as

being of the type mixed (Kenny et al., 2006). A path diagram of the model is depicted in

Figure 1. As can be seen, the Xand Yvariables are linked by four direct paths, AE

1

,AE

2

,PE

1

,

and PE

2

, where the paths from one person’sXvariable to his or her Yvariable (AE

1

and AE

2

)

are called actor effects and the paths from one person to the other person (PE

1

and PE

2

) are

called partner effects. With distinguishable members, as, for example, mother and child dyads,

there are two actor effects and two partner effects, one of each for member 1 and one of each

for member 2. With indistinguishable members, as, for example, same-sex couples, there is only

one actor effect and one partner effect. There are also two covariances, one between the two

Xvariables and another one between the two residuals, E

1

and E

2

. With manifest variables and

distinguishable members, the parameters in this model can be estimated using ordinary least

squares (OLS) regression analysis, and so standard software programs can be used to determine

the required sample size for an APIM study given the proportion of the total variance explained

or the relative increase in variance when adding a partner variable to a regression model. With

indistinguishable members, multilevel modeling (MLM) or SEM can be used, with each having

its own advantages and disadvantages (Ledermann & Kenny, 2017).

DETERMINE POWER AND SAMPLE SIZE1453