I am new to structural equation modeling.
I am wondering whether the decision to include a variable as a latent or observed variable is solely theoretical.
For example, I have experimental data and want to test whether the effect of the treatment (T) on the outcome (O) is mediated by another variable (M).
M is a variable constructed from adding 4 Likert type questions.
I am wondering what the implications are of including M as a latent (Ml) or observed (Mo) variable in a SEM. Of course the four question measure a latent construct, as do all questions. Is it, therefore, wrong to include it as an observed variable?
For those of you using Stata:
(a) sem (T -> O) (T-> Ml, ) (Ml-> O, ) (Ml-> Mo, ), latent(Ml) nocapslatent
(b) sem (T-> O, ) (T-> Mo, ) (Mo-> O, ), nocapslatent
I would also be interested in the statistical/technical differences between these alternatives.
Thanks in advance
Hi Hendrik,
beyond what James that (with what I 100% concur), I would add three things.
Firstly, fully specifying a measurement model precisely clarifies, communicates, and tests your assumption that the four measures are indeed exchangable, but equally valid reflections of one and the same underlying factor. That is more more rigid (and thus valuable) than a) just assuming that these assumptions are correct but to simply mesh the items together and b) than traditional approaches to (exploratory) factor analysis or (worse) PCA that served to "reduce complexity" or achieve convenience. To test this rigid structure, you should really test these implications, accept and follow the results of this test. If the test fails, perhaps your idea of a single latent variable is wrong and you identify causally more potent pathways via a more specific latent variable (which the four indicators measure).
Secondly, estimating a latent variable helps to reduce measurement error - beyond the good ole reliability issue (note: In SEM, measurement error is more than reliability and relates more to the overall issue of validity.
Thirdly, it is interesting that you intend to combine SEM with experimental data and a mediator process model as I work on this very issue myself these days. Note, that by including a mediator in a experimental model has a big advantage but at the same time a big disadvantage and a big danger:
a) The advantage is that you investigate the process by which the experimental treatment works. The mediator is, hence, a manipulation check and informs what the treatment does. By that way you are able to surprisingly observe direct effects that may reflect alternative processes other the theoretically proposed effect or experimenter bias/ demand characteristics. Classical ANOVA is not able to reveal this
b) The big disadvantage, however, is that you destroy all the positive consequences of the randomization. The effect of the treatment on the mediator is secured by the randomization but the relationship between the mediator and the outcome may be the target of omitted confounders or reverse causation. And if the downstream effect (M-->Y) is biased, then the indirect effect of T on Y is also biased - despite the randomization. That means that you may think about using instrumental variable techniques. If T has no direct effect on Y, than T itself may act as an instrument - allowing to estimate the error covariance between M and Y. The significance of this error covariance is a test of the endogeneity of M as well as secures the M-->Y effect of being biased.
If T has either a weak effect on M or an additional effect on Y, then you need some additional instruments for M (i.e., variables that have solely an effect on M but not on Y).
HTH
Holger
An interesting question! :-) I would suggest that the issue here is less to do with SEM and more to do with measurement - after all the issues of latent vs. observed measures, their meaning, utility, and construction extend beyond SEM to all quantitative research. The question I'd be asking myself in your place is, "to what extend is the theoretical construct adequately measured by the four observed variables rather than by a theoretical construct that lies unseen and which is generating this four observed measures?". For example, many psychological constructs are unobserved and so rely on latent (or, "high inference") measurement (personality, cognitive ability, behavioral disorders etc). By contrast, the educational construct of "educational attainment" can be measured from observed variables ( "low inference measurement"). The consequences of the subsequent use of either form of variable/measure within SEM tests of mediation are much more technical by comparison. That said, if you believe (or reviewers) believe that you have an underlying latent construct yet you decide to test mediation with observed measures... well then that will prompt disagreement and debate.
Good luck with your statistics!
Hi Hendrik,
beyond what James that (with what I 100% concur), I would add three things.
Firstly, fully specifying a measurement model precisely clarifies, communicates, and tests your assumption that the four measures are indeed exchangable, but equally valid reflections of one and the same underlying factor. That is more more rigid (and thus valuable) than a) just assuming that these assumptions are correct but to simply mesh the items together and b) than traditional approaches to (exploratory) factor analysis or (worse) PCA that served to "reduce complexity" or achieve convenience. To test this rigid structure, you should really test these implications, accept and follow the results of this test. If the test fails, perhaps your idea of a single latent variable is wrong and you identify causally more potent pathways via a more specific latent variable (which the four indicators measure).
Secondly, estimating a latent variable helps to reduce measurement error - beyond the good ole reliability issue (note: In SEM, measurement error is more than reliability and relates more to the overall issue of validity.
Thirdly, it is interesting that you intend to combine SEM with experimental data and a mediator process model as I work on this very issue myself these days. Note, that by including a mediator in a experimental model has a big advantage but at the same time a big disadvantage and a big danger:
a) The advantage is that you investigate the process by which the experimental treatment works. The mediator is, hence, a manipulation check and informs what the treatment does. By that way you are able to surprisingly observe direct effects that may reflect alternative processes other the theoretically proposed effect or experimenter bias/ demand characteristics. Classical ANOVA is not able to reveal this
b) The big disadvantage, however, is that you destroy all the positive consequences of the randomization. The effect of the treatment on the mediator is secured by the randomization but the relationship between the mediator and the outcome may be the target of omitted confounders or reverse causation. And if the downstream effect (M-->Y) is biased, then the indirect effect of T on Y is also biased - despite the randomization. That means that you may think about using instrumental variable techniques. If T has no direct effect on Y, than T itself may act as an instrument - allowing to estimate the error covariance between M and Y. The significance of this error covariance is a test of the endogeneity of M as well as secures the M-->Y effect of being biased.
If T has either a weak effect on M or an additional effect on Y, then you need some additional instruments for M (i.e., variables that have solely an effect on M but not on Y).
HTH
Holger
Thank you both for your answers.
Holger,
The point you raise about the disadvantage of this procedure is very interesting. I wasn't aware of the fact, that the relation between Mediator and outcome being correlational affects the possibility to infer causation between Treatment and Outcome as soon as I include M as a mediator. It makes intuitive sense to me although I must say that I am not able to fully understand the logic behind it yet.
Actually, with respect to my experiment I want to answer the question, whether subjects that react to the treatment (T) in a certain way with respect to their behavior (O), are also the subjects that react to the treatment (T) in a certain way with respect to M.
Intuitively, I thought this question was similar to: Is the effect of T on O partially mediated by M.
However, I have the feeling that this question could also be posed as Does the effect of T on O depend on M, which sounds rather like a mediation/interaction.
Do I maybe need to phrase my question better in order to be able to better determine the statistical procedure I need?
So far, my analysis dealt with the impact of T on M, as well as with the impact of T on O, both separated from one another. No I want to 'go one step further' and see of the effect of T on O is 'caused' by the effect of T on M (cause is the wrong word, since I cannot establish causality of M on O).
Hi Hendrik
you see, SEM forces you to clearly think about the causal net you have in mind.
a) The phrase "whether subjects that react to the treatment (T) in a certain way with respect to their behavior (O), are also the subjects that react to the treatment (T) in a certain way with respect to M" sounds a bit vague and could also mean that T causes M as well as O. Such a causal model would imply T having effects on M and O, with M and O either being conditionally unrelated (they correlate only because T is their common cause) or related (they my have omitted common causes or some kind of causal relationship. If such an causal relationship implies that M causes O, then this model is a partial mediation model, in which T affects O both indirectly and directly. As this model is saturated, you cannot really say something about causes beyond that T causes M and O. The effect of M on O and henec the indirect effect of T on O via M is causally not identified.
b) When you think that the effect of T on O depends on M, than M is a MODerator - not mediator
c) the reason why inclusion of a mediator destroys (partially) the randomization is the potential of confounding despite randomization. Imagine, M is knowledge, and O is some kind of cognitive task. T is a training program. In this case, it is very likely that intelligence influences both knowledge as well as the performance of the task. Hence, it is a omitted common cause (confounder) of both variables. As a result, the effect of knowledge on performance is biased. More formally, the estimated effect is a + b*c, where "a" is the true effect of knowledge on the performance, "b" is the effect of Intelligence on knowledge and "c" is the effect of intelligence on performance. Even if T is randomized and its effect on M is unbiased, the indirect effect will be biased as it is the product of both effects. If "d" is the unbiased effect of T on M, the indirect TRUE effect is d*a, but due to the confouding of the downstream part of the model, the estimated indirect effect ist d*(a+b*c). This problem can be solved by estimating the error variance between M and O, because this error covariance will catch up the b*c component of the relationship between M and O. However, you need enough information (input variables) in order to identify the error covariance and the input needs to be strong. If the effect of T is strong, then T may allow estimating the error covariance.
You may take a look into my (German) book on SEM where all this is explained in more detail.
HTH
Holger
- Badges
- Science topic
- Similar topics
- Physical Sciences
- Materials Science
- Materials
- Inorganic Materials
- Ceramics