Setting Up a Measurement Model

[mmayfield]

Dear Smart PLS forum members,

I am writing for suggestions about setting up a measurement model using Smart PLS. I am testing a scale's measurement properties, and I wanted to use PLS for this purpose. When I have used covariance structural equation modeling for this procedure, I have set up a measurement model (i.e. a model with no dependent/endogenous variables). However, with Smart PLS I have to have some variable as a dependent/endogenous variable.

What I have done initially is to set up a second order factor model. I used the second order factor as the independent variable, and treated the first order factors as the dependent variables. The method seems to work well, but I wondered if there was a better way to go about the procedure.

Also, one issue that has come up is that while the overall model seems to fit the data well (good alphas, t-tests, R-squares, loadings, cross-loadings, AVEs, etc.), the second-order factor's AVE is low – around 0.37. Is this result to be expected in a measurement model? If not, does is really pose a problem since the only reason I am including a second order factor is to get the model to run?

As an alternative (more or less to see what would happen) I also set up the variables in a “chain.” My first variable influences my second, third, and fourth variable, the second variable influences the third and fourth, and so on. This technique seems to work ok as well, but seems odd to someone who is used to non-recursive relationships between measurement model latent variables.

Thanks in advance for your help in this matter. All feedback will be appreciated.

Sincerely,
Milton Mayfield

[tomcurl]

Hello,

thanks for your post. I am facing exactly the same problem. Re-use of first-order construct indicators for operationalizing the second-order construct, "just to make the model" work and produce output, results in low AVE of the second order construct, as well as low outer loadings and outer weights of the indicators on that second order construct.

Apart from that, my model works just fine, i.e., R-square, communalities, redundancies, outer loadings and outer weights of manifest indicators on first-order constructs...all that is well above the requirements established in the literature.

Can I just ignore the low outer loadings and outer weights, as well as low AVE of that second-order construct, as I did not really specify a measurement model for it anyways, but instead just re-used the first order manifest indicators to make the model work?

Can anybody help here, please?

Best regards,

Thomas

[jjsailors]

Hello,

thanks for your post. I am facing exactly the same problem.

For both of you, do you have alternative measures for the scales you are developing? If so, create your models with those as the dependent variables.

If you lack known alternatives, then what other variables are your factors thought to predict?

As you've observed, the measurement model is not independent from the structural model in PLS.

BTW, how many first order factors do you have? I would expect that with a small number of first order factors you might not see the effects you describe, but would be more likely to as the number of first order factors increases. Just curious.

Regards,
John

[tomcurl]

John,

thanks for your post. Indeed, I have 11 indicators. This could be part of the problem. In order to avoid the re-use of the indicators, I have eliminated the construct for which this would have to be the case.

Instead, the first order latent variables (service benefits) are now directly connected to a second order latent variable (service quality) that is operationalized by means of two (other) manifest indicators. I discovered that the use of a second order latent variable mediating between the service benefits (first order) and service quality (before third order, now second order), does not improve the quality of the structural model at all.

I do have another question though: in my mew model, bootstrap t-values of the paths from the first order benefits to the second order service quality construct are below 2 (sample size 500). At the samw time, the R square for service quality is high and other quality criteria (communality, redundancy, cronbach alpha, etc.) are also acceptable. The problem I am facing is multicollinearity I suppose.

How serious is this? Can I reduce it by eliminating the paths with the lowest values?

Regards

[jjsailors]

bootstrap t-values of the paths from the first order benefits to the second order service quality construct are below 2 (sample size 500). At the samw time, the R square for service quality is high and other quality criteria (communality, redundancy, cronbach alpha, etc.) are also acceptable. The problem I am facing is multicollinearity I suppose.

How high is the correlation among the benefits constructs? If it is multicollinearity that is the issue, then its seriousness is a matter of what your overall objective is. If you want to understand the influence of the different benefits to quality, then it's serious. Alternatively, if you only want to maximize your prediction of quality (for example, if this is an applied project), then it's not really an issue.

I suspect, given that you're a doctoral student, that it's the former and not the latter. That being the case, I think you have some work to do to have benefit constructs that are more distinct from one another.

If you do an exploratory factor analysis of the benefit indicator variables, how many factors do there appear to be? How much larger is the first eignevalue than the others? If one eigenvalue is really dominant, it may suggest that you'll encounter this sort of multicollinearity problem.

[tomcurl]

John,

thanks for your comments. You guessed correctly - the objective is indeed to determine the influence of various benefits on service quality.
Therefore, I have to find a way to reduce multicollinearity (yes, some of the LV correlations between the benefits are as high as 0.80).

I recurred to the method of eliminating insignificant paths (t-value<2 as indicated by the bootstrap algorithm). Successively eliminating insignificant paths works well and leaves me with the significant ones whose influence on service quality I can then interpret.

Additionally, I am testing for interaction effect in my model. I have 4 moderators, and I test their influence on satisfaction (which is the higher order construct in my model that is determined by service quality) one by one, as I found out that testing for all four at the same time leads nowhere. For testing, I use the model with the significant paths, from which the benefits with insignificant paths to service quality have already been eliminated.
Unfortunately even so, I am not able to detect any significant interaction effects (using standardization of indicator values before path indicator multiplication).

Has anyone been luckier with his measurement of interaction effects?

Best regards,

Thomas

[jjsailors]

...to the method of eliminating insignificant paths (t-value<2 as indicated by the bootstrap algorithm). Successively eliminating insignificant paths works well and leaves me with the significant ones whose influence on service quality I can then interpret...

Unfortunately, I suspect that you're also eliminating significant paths. Let's say you've kept the path from construct A to construct C, which is significant, but have eliminated the path from construct B to construct C, which appeared non-significant. If in fact B is highly correlated with A, then B --> C is probably really significant too (if you run the model with B --> C but without A --> C it probably would be significant).

In essence, A and B are not distinct constructs. In PLS, since the constructs are linear combination of observed variables with the calculation of indicator weights impacted by the structural paths, this shouldn't be passed over too quickly.

I would recommend that you take your staring model, the one with the nonsignificant paths from bootstrapping and run a factor analysis on the latent variable scores to see which of your constructs should be combined. Redefine your measurement and structural model according and see what you get.

Good luck!