Latent Variables and Structural Equations Modeling

8 July 2006 at 12:33 am 3 comments

| Peter Klein |

Among my PhD students I note an increasing interest in structural equations modeling (SEM), particularly for working with latent variables. One student’s dissertation uses SEM to study the effect of the institutional environment on entrepreneurship, treating entrepreneurship as a latent variable and using measures of new business starts, patent filings, and the like as the corresponding manifest variables. Another student is using SEM to examine free-riding among members of a large cooperative, with various observable behaviors serving as indicators for the latent variable free-riding.

More generally, SEM is becoming a standard tool in management, where abstract concepts like trust, knowledge, capabilities can (potentially) be modeled as latent variables in a system of equations. Indeed, when I visited Nicolai in his office in Copenhagen a couple of weeks ago, the first thing I noticed on his desk was a LISREL manual, prominently displayed on the corner. (He assures me it is not for show.)

What to make of this? Structural equations models can certainly be more flexible than classical linear regression models (which, technically speaking, are a subset of SEM). Path diagrams can be illuminating, though as an economist I’m uncomfortable with hypothesized relationships that aren’t closely connected to a priori theory. On the other hand, SEM tends to constrain individual relationships to be simple linear ones, and (as far as I know) SEM cannot easily handle panel data, probabilistic relationships, and other complexities. Most important, finding empirical support for a hypothesized set of paths does not, contrary to what SEM enthusiasts sometimes suggest, establish causality.

SEM does not seem to have attracted as much attention in economics. My guess is that economists see the path diagrams as ad hoc, as a poor substitute for “real” deductive theory. And economists seem less comfortable with latent variables. Arnold Kling, for example, has written a series of posts on EconLog criticizing economic research on happiness. In one post he writes:

My basic issue with happiness research, which arises in this paragraph, is that it does not have an operational definition of what it is measuring. . . . I think that statements like “X makes people happy” are faux-empirical. You have no business making such claims when you don’t have a clear definition of happiness to begin with.

An SEM enthusiast would have no problem with these data; simply treat happiness as a latent variable and off you go.

Entry filed under: - Klein -, Entrepreneurship, Institutions, Management Theory, Methods/Methodology/Theory of Science, Strategic Management, Theory of the Firm.

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3 Comments Add your own

  • 1. Bob V  |  9 July 2006 at 8:10 am

    Numbering the critiques:

    1. Path diagrams are supposed to be based on a piori theory as much as the models that researchers generate with the intention of being tested by any other method. I haven’t noticed any less theoretical development in research using SEM, but even if there is, there is nothing that prevents the researcher from creating a model based on a priori theory.

    2. Panel data can be handled by a technique called latent growth modeling. You might have to be clever to handle a probabilistic relationship.

    3. Yes, empirical support for an SEM model does not establish causality. But empirical support for *any* model does not establish causality. This is a critique of empirical research, not of any one technique such as SEM. Ironclad proof only exists in the world of deduction.

    4. Latent variables are in fact strange critters. However, our inability to measure a variable directly should not preclude us from attempting to conduct research. Otherwise, empirical research is limited making claims like “X makes people fill out a response on a survey.” The reader must then assume that the response is indicative of happiness. It is better to go ahead and make the claim “X makes people happy” and use a technique like factor analysis to give the consumer of the research a basis for evaluating whether the survey items really do respresent happiness or not.
    (Note that the researcher must still come up with a clear definition of happiness. I do not know if the happiness research does this or not. My point is that latent variables cannot be rejected wholesale.)

  • 2. Fabio Rojas  |  9 July 2006 at 9:23 pm

    Resistance to latent variables, and SEM more generally, is bizarre. Path diagrams ad hoc? Not in principle – a good researcher will have a good reason for each link in the diagram. Any statistical technique is ad hoc in the wrong hands.

    Undefined latent variables? Not a problem either – there are lots of variables in life that are hard to precisely define, but we can measure anyway. Intelligence, healthiness, athleticism, creativity, etc. You can’t easily define any of these, but if they exist, they should be associated with a bundle of similar variables. (e.g., high IQ means you answer lots of test questions correctly)

    This is where good statistics comes into play – you treat your latent variable as a hypothesis and SEM can tell you if indeed the data support the hypothesis of a single latent variable affecting all your measurable variables.

    Economists resistance to SEM is just a sign of the weird intellectual culture in that profession. The economists learn one tool and do it to death and seem completely blind to anything else. It’s very strange.

    Their statistics courses deal almost exclusively with OLS and a little time series. Mention something as simple as ANOVA and they stare at you blindly. Factor analysis? Never heard of it. Clustering? Don’t even go there. Log linear modeling? Might as well be Greek.

    One of the big benefits of taking statistics outside an econ or management program is that quickly learn about the wide world of statistics and not just OLS/time series. If economists bothered to look around, they would quickly see that there’s a whole world of tools out there.

  • 3. Bo Nielsen  |  12 July 2006 at 4:22 am

    I agree with the defense of SEM – to me, what makes the difference is the use of each statistical tool. For instance, testing competing models in SEM yield more robust results than not testing competing models (just like in any other type of statistics). The fact that some researchers do not go through the trouble of adequately defining theoretical constructs and relationships before testing is a weakness not only in SEM. The criticism of SEM is often be based on poor understanding on the part of the opponent. For instance, not only can SEM model time series problems via growth models (the advanced method) but also more simply by comparing models over the years (multiple group comparision I think it is called). SEM allows for multi-level testing, longitudinal and latent growth curve analysis, as well as extended applications such as hierarchical and multitrait-multimethod decompositions.

    SEM allows for modeling of the measurement error, something that economists seem to assume away (or ignore). An essential feature of most other statistics applications is that only the dependent variable or the observed response is assumed to be subject to measurement error or other uncontrolled variation. That is, there is only one random variable in the picture. Part of this difference may stem from the fact that, to my knowledge, SEM was originally developed with primary data testing in mind – that is modeling of complex processes, whereas economists have a long tradition of utilizing secondary datasets to test their relationships.

    Much of the confusion or opposition seems to be related to the use of latent variables in SEM – a somewhat messy (yet clever) way of accounting for the unobservable variables by using BOTH proxies and accounting for the measurement error in all variables, whereas traditional economics research only seem to use proxies for these variables (admittedly a bit black-and-white, but you get the point).

    Admittedly, some SEM research in management is poorly done – and for a while we saw a tendency of top journals favoring SEM models with less theoretical rigor. As SEM becomes better understood and more widely used (and it has existed for almost 80 years! and been widely used in psychology and natural sciences) in management, we should see a tendency toward more rigorous use. One problem is that some scholars tend to violate the strive for parsimony – many studies in management utilize far more complex statistical modeling than is needed – perhaps in an effort to disguise the fact that their paper lacks rigorous theory etc.

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