Comparing Structural Equation Modelling to Multiple Regression
The use of structural equation modelling (SEM) has grown steadily in the market research arena since it first appeared in papers in the late 1960s. Described as a second generation technique[1], SEM relegates the long standing ubiquitous traditional techniques such as ANOVA, MANOVA, linear regression etc. to ‘first generation’.
Does this mean that SEM, the ‘new kid on the block’ has brought with it the beginning of the demise of the loyal, first generation techniques, specifically regression analysis?
Are the advantages of SEM such that they leave no place for multiple regression analysis? Or does the tried and true regression analysis have its own advantages over SEM that will ensure its survival in the world of data analysis?
Before addressing these questions, a brief introduction of SEM is warranted.
SEM is a sophisticated tool that estimates coefficients in a set of linear structural equations. The components in these equations comprise observed/measured variable and/or unmeasured, latent variables. Although not observed, these latent variables are related to the observed variables. The underlying structure assumed in SEM is a causal one among a set of latent variables with the observed variables taking the role of being their indicators. The latent variables may be linearly related to the indicator variables or may themselves be mediating variables in a causal chain.[2] SEM has a unique ability to not only examine multiple relationships of dependence but also, and at the same time, examine numerous dependent variables.
Compared to regression and factor analysis, the field of SEM is relatively young with its first appearance in papers not occurring until the late 1960’s. Although introduced into strategy literature in 1984, SEM has only more recently become popular in this field. Interestingly, prior to 1995 only five studies using SEM were published in Strategic Management Journal. From 1998 – 2002 this figure rose to 27.
What would be considered the primary advantage of SEM is its ability to assess all pathways of a relationship simultaneously even though the dependent variable may become the indicator in a subsequent pathway. With regression analysis, such a model would have to be analysed in separate regression runs where an allocated dependent variable played no other role. When you are able to test all pathways at once as you are with SEM, there are no statistical issues with a lack of connection between runs as you have with regression analysis.
Other advantages of SEM are listed as follows:[3]
Given the many strengths of SEM then, is there still a place for linear regression?
As with any statistical tool, the benefits of SEM are enjoyed only if the technique is properly applied. Given the relative ‘youth’ of SEM, this is not always the case. Reviews of SEM usage in the fields of organisational behaviour, MIS, marketing and logistics have revealed some series flaws. It seems that there are still some ‘teething’ problems to be rectified, so whilst SEM clearly has advantages over regression analysis, it seems that these come with trade-offs in the form of inexperienced application and interpretation.
Where the objective of relational analysis is exploratory, regression analysis is the most appropriate technique to use. This is because the structural model in SEM is quite complex and usually there are a large number of statistically valid alternative models that can be supported by the same data. As a result, SEM is better used as a confirmatory rather than exploratory technique.
Another scenario in which regression analysis might the chosen technique over SEM is for historical comparative purposes. That is, the comparison of current findings to those from other earlier studies that traditionally used regression. In this way, researchers who wanted to add to the research tradition or add to longitudinal studies would find it more conducive to use linear regression.
Further, SEM requires larger sample sizes than does multiple linear regression. For models with 10 – 15 indicators, SEM requires 200 – 400 observations. Even when applying the most conservative rule of thumb, multiple regression requires only 100- 150 under the same circumstances. As a result, regression analysis can save the day when there are sample size limitations. Regression analysis should also be considered where there are problems in meeting the normality assumptions of SEM. And again, regression may be the preferred technique when the measures have high reliability resulting in less concern about measurement error.
So, whilst the ‘new kid on the block’, SEM, certainly has numerous advantages over regression analysis, it does not replace it. Depending on the conditions of the data under study, regression analysis may be the better suited technique. As always, it is a matter of the researcher being aware of the advantages and limitations of each technique and then choosing the one that best matches the characteristics of the data.
[For an excellent, detailed discussion of SEM in Market Research, see Scott MacLean’s article, “Structural Equation Modelling in Market Research” referred to in footnote one.]
[1] Bagozzi, R.P and C. Fornell (1982), “Theoretical Concepts, Measurement and Meaning”, Vol. 2C Fornell (Ed). A Second Generation of Multivariage Analysis: Praeger, pp. 5 – 23.
[2] Scott MacLean, Kevin Gray, “Structural Equation Modelling in Market Research”, Australasian Journal of Market & Social Research. Volume 6, No 1, January, 1998.
[3] Structural Equation Modelling, Statnotes: Topics in Multivariate Analysis, by G. David Garson
Does this mean that SEM, the ‘new kid on the block’ has brought with it the beginning of the demise of the loyal, first generation techniques, specifically regression analysis?
Are the advantages of SEM such that they leave no place for multiple regression analysis? Or does the tried and true regression analysis have its own advantages over SEM that will ensure its survival in the world of data analysis?
Before addressing these questions, a brief introduction of SEM is warranted.
SEM is a sophisticated tool that estimates coefficients in a set of linear structural equations. The components in these equations comprise observed/measured variable and/or unmeasured, latent variables. Although not observed, these latent variables are related to the observed variables. The underlying structure assumed in SEM is a causal one among a set of latent variables with the observed variables taking the role of being their indicators. The latent variables may be linearly related to the indicator variables or may themselves be mediating variables in a causal chain.[2] SEM has a unique ability to not only examine multiple relationships of dependence but also, and at the same time, examine numerous dependent variables.
Compared to regression and factor analysis, the field of SEM is relatively young with its first appearance in papers not occurring until the late 1960’s. Although introduced into strategy literature in 1984, SEM has only more recently become popular in this field. Interestingly, prior to 1995 only five studies using SEM were published in Strategic Management Journal. From 1998 – 2002 this figure rose to 27.
What would be considered the primary advantage of SEM is its ability to assess all pathways of a relationship simultaneously even though the dependent variable may become the indicator in a subsequent pathway. With regression analysis, such a model would have to be analysed in separate regression runs where an allocated dependent variable played no other role. When you are able to test all pathways at once as you are with SEM, there are no statistical issues with a lack of connection between runs as you have with regression analysis.
Other advantages of SEM are listed as follows:[3]
- more flexible assumptions (particularly allowing interpretation even in the face of multicollinearity)
- ability to construct unobservable latent variables
- use of confirmatory factor analysis to reduce measurement error by having multiple indicators per latent variable
- ease of use of graphical modelling interface
- the ability to test models with multiple dependents,
- the ability to model mediating variables
- the ability to model error terms
- the ability to test coefficients across multiple between-subjects groups
- the ability to handle difficult data (eg time series with auto-correlated error, non-normal data, incomplete data)
Given the many strengths of SEM then, is there still a place for linear regression?
As with any statistical tool, the benefits of SEM are enjoyed only if the technique is properly applied. Given the relative ‘youth’ of SEM, this is not always the case. Reviews of SEM usage in the fields of organisational behaviour, MIS, marketing and logistics have revealed some series flaws. It seems that there are still some ‘teething’ problems to be rectified, so whilst SEM clearly has advantages over regression analysis, it seems that these come with trade-offs in the form of inexperienced application and interpretation.
Where the objective of relational analysis is exploratory, regression analysis is the most appropriate technique to use. This is because the structural model in SEM is quite complex and usually there are a large number of statistically valid alternative models that can be supported by the same data. As a result, SEM is better used as a confirmatory rather than exploratory technique.
Another scenario in which regression analysis might the chosen technique over SEM is for historical comparative purposes. That is, the comparison of current findings to those from other earlier studies that traditionally used regression. In this way, researchers who wanted to add to the research tradition or add to longitudinal studies would find it more conducive to use linear regression.
Further, SEM requires larger sample sizes than does multiple linear regression. For models with 10 – 15 indicators, SEM requires 200 – 400 observations. Even when applying the most conservative rule of thumb, multiple regression requires only 100- 150 under the same circumstances. As a result, regression analysis can save the day when there are sample size limitations. Regression analysis should also be considered where there are problems in meeting the normality assumptions of SEM. And again, regression may be the preferred technique when the measures have high reliability resulting in less concern about measurement error.
So, whilst the ‘new kid on the block’, SEM, certainly has numerous advantages over regression analysis, it does not replace it. Depending on the conditions of the data under study, regression analysis may be the better suited technique. As always, it is a matter of the researcher being aware of the advantages and limitations of each technique and then choosing the one that best matches the characteristics of the data.
[For an excellent, detailed discussion of SEM in Market Research, see Scott MacLean’s article, “Structural Equation Modelling in Market Research” referred to in footnote one.]
[1] Bagozzi, R.P and C. Fornell (1982), “Theoretical Concepts, Measurement and Meaning”, Vol. 2C Fornell (Ed). A Second Generation of Multivariage Analysis: Praeger, pp. 5 – 23.
[2] Scott MacLean, Kevin Gray, “Structural Equation Modelling in Market Research”, Australasian Journal of Market & Social Research. Volume 6, No 1, January, 1998.
[3] Structural Equation Modelling, Statnotes: Topics in Multivariate Analysis, by G. David Garson
