Does the number of manifest measures affect the model result
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jahoosafat
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Does the number of manifest measures affect the model result
In factor analysis, it's well known that if you generate a factor from, for instance, 8 variables and include it in a regression with another factor generated from, let's say, 2 variables ... then the first factor is almost definitely going to have a much stronger association with the dependent variable. Does something similar happen in PLS? Does the number of manifest variables in an outer model for a latent variable affect how strong of a predictor it will be in the PLS causal model?
Jeff
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jahoosafat
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Hi Hengky - Thanks, but I don't think that answers my question. I'm not asking what is a sufficient number of indicators for a good model. I'm asking if PLS "favors" latent variables that have large numbers of indicators over latents with smaller numbers of indicators in the same model. So, if we had a 3 latent variable model:
X -> Y <- Z
And X had 10 indicators while Z had 2 indicators. If I did a principal components regression, X would almost certainly be found to be the stronger predictor of Y. Empirically, do we find the same sort of thing in PLS or no?
Cheers,
Jeff
X -> Y <- Z
And X had 10 indicators while Z had 2 indicators. If I did a principal components regression, X would almost certainly be found to be the stronger predictor of Y. Empirically, do we find the same sort of thing in PLS or no?
Cheers,
Jeff
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Hengkov
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Hi Jeffry,
If you have models is complex => large indicators is good (optimal predict),
But If you have models is simple => small indicators no problem (with minimal indicator 3 items for each construct, some literature suggest > 5 items for evaluation outer model).
Note: number of resampling is large for correct SE.
Regards,
Hengky
If you have models is complex => large indicators is good (optimal predict),
But If you have models is simple => small indicators no problem (with minimal indicator 3 items for each construct, some literature suggest > 5 items for evaluation outer model).
Note: number of resampling is large for correct SE.
Regards,
Hengky
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jahoosafat
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Still not the question. What I am asking about is the comparative predictive strength of latents with many indicators vs. latents with few indicators IN THE SAME MODEL. Again, empirically, if you do a simple principle components regression, you'll almost always find that the latents with many indicators would be stronger predictors of some dependent variable as compared to latents with very few indicators. The question is whether PLS has the same tendency. Maybe someone else could address this question.
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Marcel_Dijkstra
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It all depends on the structure in the data, i.e. whether high scores in X corresponds with high (or low) scores in Y. To illustrate this take it to the extreme; a signle indicator latent X as compared to a 10 indicator latent Z.
Now suppose X is smoking behaviour, Z is a schizofrenia scale and your dependent latent Y is lung cancer, then most probably the relationship between X and Y is likely to be stronger than the relationship between Z and Y.
But you are right in general a latent with more indicator represents a more 'stable' measurement than a single latent indicator. The latter has just a larger error term by the very definition. And hence it will be more difficult for a single indicator latent to reach significance. The fluctuations in the regression coefficient around the 'true' value is just greater. That is the same as saying that one case has more influence over the latent score in a signle indicator latent than one case has when you have 10 measurements. A fluke in one of the indicators in a 10 indicator latent will have less effect because the latent score is the weighted average of all 10 scores.
I hope this gives you an answer to your question.
Now suppose X is smoking behaviour, Z is a schizofrenia scale and your dependent latent Y is lung cancer, then most probably the relationship between X and Y is likely to be stronger than the relationship between Z and Y.
But you are right in general a latent with more indicator represents a more 'stable' measurement than a single latent indicator. The latter has just a larger error term by the very definition. And hence it will be more difficult for a single indicator latent to reach significance. The fluctuations in the regression coefficient around the 'true' value is just greater. That is the same as saying that one case has more influence over the latent score in a signle indicator latent than one case has when you have 10 measurements. A fluke in one of the indicators in a 10 indicator latent will have less effect because the latent score is the weighted average of all 10 scores.
I hope this gives you an answer to your question.
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jahoosafat
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Diogenes
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Hi,
In others words:
1) LISREL (SEM – covariance based) is not biased = the correlation between two LV will be estimated correctly.
2) PLS-PM is “consistent at large” = correlation between LV are underestimated. The correlations (or path coefficients) are estimated from the LV scores, that are a weighted mean of the indicators, and the measurement error are included in the score calculation.
Nunnally and Bernstein named this effect as “attenuation of the correlation”.
Lohmöller, Wold and Chin remember us, in many articles, that PLS is “consistent at large”. With more indicators, greater will be the reliability e lesser will be the attenuation.
Best regards,
Bido
In others words:
1) LISREL (SEM – covariance based) is not biased = the correlation between two LV will be estimated correctly.
2) PLS-PM is “consistent at large” = correlation between LV are underestimated. The correlations (or path coefficients) are estimated from the LV scores, that are a weighted mean of the indicators, and the measurement error are included in the score calculation.
Nunnally and Bernstein named this effect as “attenuation of the correlation”.
Lohmöller, Wold and Chin remember us, in many articles, that PLS is “consistent at large”. With more indicators, greater will be the reliability e lesser will be the attenuation.
Best regards,
Bido