The EffectLiteR Approach for Analyzing Average and Conditional Effects

ABSTRACT

We present a framework for estimating average and conditional effects of a discrete treatment variable on a continuous outcome variable, conditioning on categorical and continuous covariates. Using the new approach, termed the EffectLiteR approach, researchers can consider conditional treatment effects given values of all covariates in the analysis and various aggregates of these conditional treatment effects such as average effects, effects on the treated, or aggregated conditional effects given values of a subset of covariates. Building on structural equation modeling, key advantages of the new approach are (1) It allows for latent covariates and outcome variables; (2) it permits (higher order) interactions between the treatment variable and categorical and (latent) continuous covariates; and (3) covariates can be treated as stochastic or fixed. The approach is illustrated by an example, and open source software EffectLiteR is provided, which makes a detailed analysis of effects conveniently accessible for applied researchers.

Keywords:

• Average and conditional effects
• multigroup structural equation modeling
• moderation
• stochastic regressors
• interactions

Article information

Conflict of Interest Disclosures: Each author signed a form for disclosure of potential conflicts of interest. No authors reported any financial or other conflicts of interest in relation to the work described.

Ethical Principles: The authors affirm having followed professional ethical guidelines in preparing this work. These guidelines include obtaining informed consent from human participants, maintaining ethical treatment and respect for the rights of human or animal participants, and ensuring the privacy of participants and their data, such as ensuring that individual participants cannot be identified in reported results or from publicly available original or archival data.

Funding: This work was not supported.

Role of the Funders/Sponsors: None of the funders or sponsors of this research had any role in the design and conduct of the study; collection, management, analysis, and interpretation of data; preparation, review, or approval of the manuscript; or decision to submit the manuscript for publication.

Acknowledgements: The ideas and opinions expressed herein are those of the authors alone, and endorsement by the authors’ institutions is not intended and should not be inferred.

Notes

1 Note that it would also be possible to compare innovative therapy versus conventional therapy (X = 2 vs. X = 1) by choosing another coding.

2 This model as presented here with a saturated Poisson model for group sizes is implemented in lavaan (Rosseel, 2012) in versions ≥0.5-16. We chose a Poisson model with the canonical log link because it leads to a relatively easy-to-compute likelihood and does not require constrained optimization. A similar model using a multinomial model for group sizes is available in Mplus (Muthén & Muthén, 1998–2012) via the KNOWNCLASS option. The KNOWNCLASS option was first used to analyze average effects by Kröhne (2009) for cases without categorical covariates and was extended by Dietzfelbinger (2014), who also provides automatic generation of software code.

3 The term generalized ANCOVA refers to an ANCOVA with interactions between treatment and covariates, which is typically implemented using a multigroup structural equation modeling approach. It has been introduced by researchers at the Department of Methodology and Evaluation Research under supervision of Rolf Steyer, and there are several theses about this topic (e.g., Dietzfelbinger, 2014; Flory, 2008; Hartenstein, 2005; Kröhne, 2009; Nagengast, 2006). Generalized ANCOVA is also described in the software manual for EffectLite (Steyer & Partchev, 2008).

The consideration of just a single covariate K is not a restriction to the number of categorical covariates, because K may be obtained by unfolding multiple discrete covariates K₁, K₂, …; that is, the values of K then represent all possible combinations of values of multiple categorical covariates.

4 An exception to this rule is a controlled experiment where dose is varied systematically along a continuum.