The Impact of Scaling Methods on the Properties and Interpretation of Parameter Estimates in Structural Equation Models with Latent Variables

Klopp, Eric; Klößner, Stefan

doi:10.1080/10705511.2020.1796673

Cited by 13 publications

(17 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Once the metric of a measured variable has been set and fixed, the measured variable and the involved parameters are no longer arbitrary. It is true that any parameter involving a latent variable can be thought of as an algebraic transformation of an unobserved population quantity (Klopp & Kl€ oßner, 2021); however, the same applies to any parameter involving a measured variable because of the measurement scales' arbitrariness (Markus & Borsboom, 2013, Chapter 2). Fortunately, there are ways to deal with the arbitrariness of scales.…”

Section: Discussionmentioning

confidence: 99%

Structural Parameters under Partial Least Squares and Covariance-Based Structural Equation Modeling: A Comment on Yuan and Deng (2021)

Schuberth

Rosseel

Rönkkö

et al. 2022

Structural Equation Modeling: A Multidisciplinary Journal

View full text Add to dashboard Cite

In their article, Yuan and Deng argue that a structural parameter under partial least squares structural equation modeling (PLS-SEM) is zero if and only if the same structural parameter is zero under covariance-based structural equation modeling (CB-SEM). Yuan and Deng then conclude that statistical tests on individual structural parameters assessing the null hypothesis of no effect can achieve the same purpose in CB-SEM and PLS-SEM. Our response to their article highlights that the relationship they find between PLS-SEM and CB-SEM structural parameters is not universally valid, and that consequently, tests on individual parameters in CB-SEM and PLS-SEM generally do not fulfill the same purpose.

show abstract

Section: Discussionmentioning

confidence: 99%

Structural Parameters under Partial Least Squares and Covariance-Based Structural Equation Modeling: A Comment on Yuan and Deng (2021)

Schuberth

Rosseel

Rönkkö

et al. 2022

Structural Equation Modeling: A Multidisciplinary Journal

View full text Add to dashboard Cite

show abstract

“…For a particular scaling method, the estimates may differ if either a correlation or a covariance matrix is analyzed or the estimates may differ depending on the scaling method when correlation matrices are analyzed. However, standardizing estimates is invariant towards the choice of a particular scaling method (see Klopp & Klößner, 2020). In order to correctly fit a model using a correlation matrix, the constraint optimization method can be used.…”

Section: Discussionmentioning

confidence: 99%

“…As already mentioned in the introduction, the interpretation of the hypothesis when comparing unstandardized regression coefficients in Equation ( 1) is fundamentally different from the hypothesis when comparing standardized regression coefficients in Equation ( 4), and the condition from Equation (5) when they are equivalent is hardly ever met. The interpretation of an unstandardized regression coefficient is that when the explanatory variable changes one unit, then the dependent variable changes β ki units (at least in models without latent variables, in models with latent variables this interpretation is more complicated, see Klopp & Klößner, 2020). In contrast, the interpretation of a standardized regression coefficient is that when the explanatory variable changes one standard deviation, the dependent variables changes β S ki standard deviations.…”

Section: Discussionmentioning

confidence: 99%

“…Both scaling issues cause the estimated regression coefficients to depend on the given metric of the manifest variables and the scaling method used to scale the latent variable. Fortunately, the standardized regression coefficients are also invariant towards the particular applied scaling method for the latent variables (see Klößner & Klopp, 2019;Klopp & Klößner, 2020).…”

Section: Third Example Involving Latent Variablesmentioning

confidence: 99%

See 1 more Smart Citation

A Tutorial on Testing the Equality of Standardized Regression Coefficients in Structural Equation Models using Wald Tests with lavaan

Klopp¹

2019

Preprint

Self Cite

View full text Add to dashboard Cite

Comparing the effects of two or more explanatory variables on a dependent variable in structural equation models, with either manifest or latent variables, may be hampered by the arbitrary metrics which are common in social sciences and psychology. A possible way to compare the effects is the comparison of standardized regression coefficients by means of the Wald test. In this tutorial, we show how a typical textbook display of the Wald test can be used to derive a calculation for standardized regression coefficients. Moreover, we demonstrate how this can be implemented in R using the lavaan package. Additionally, we provide a convenience function that allows doing a Wald test by only setting up equality constraints. We also discuss theoretical aspects and implications when hypotheses about the equality of standardized regression parameters in structural equation models are tested.

show abstract

“…It is well known that the selection of different scaling indicators characteristically alters the means and variances of the latent variables because of the differences in the means and variances of the scaling indicators (e.g., Bollen, 1989; Klopp & Klößner, 2021; Schweizer & Troche, 2019; Schweizer et al, 2019). This is expected because by changing the scaling indicators, we are changing the units and origins of the latent variables.…”

mentioning

confidence: 99%

Selecting scaling indicators in structural equation models (sems).

Bollen¹,

Lilly²,

Luo³

2024

Psychological Methods

View full text Add to dashboard Cite

It is common practice for psychologists to specify models with latent variables to represent concepts that are difficult to directly measure. Each latent variable needs a scale, and the most popular method of scaling as well as the default in most structural equation modeling (SEM) software uses a scaling or reference indicator. Much of the time, the choice of which indicator to use for this purpose receives little attention, and many analysts use the first indicator without considering whether there are better choices. When all indicators of the latent variable have essentially the same properties, then the choice matters less. But when this is not true, we could benefit from scaling indicator guidelines. Our article first demonstrates why latent variables need a scale. We then propose a set of criteria and accompanying diagnostic tools that can assist researchers in making informed decisions about scaling indicators. The criteria for a good scaling indicator include high face validity, high correlation with the latent variable, factor complexity of one, no correlated errors, no direct effects with other indicators, a minimal number of significant overidentification equation tests and modification indices, and invariance across groups and time. We demonstrate these criteria and diagnostics using two empirical examples and provide guidance on navigating conflicting results among criteria.

show abstract

The Impact of Scaling Methods on the Properties and Interpretation of Parameter Estimates in Structural Equation Models with Latent Variables

Cited by 13 publications

References 28 publications

Structural Parameters under Partial Least Squares and Covariance-Based Structural Equation Modeling: A Comment on Yuan and Deng (2021)

Structural Parameters under Partial Least Squares and Covariance-Based Structural Equation Modeling: A Comment on Yuan and Deng (2021)

A Tutorial on Testing the Equality of Standardized Regression Coefficients in Structural Equation Models using Wald Tests with lavaan

Selecting scaling indicators in structural equation models (sems).

Contact Info

Product

Resources

About