In a study of reliability I am using Cronbach ´alpha and GSEM (generalizing structural equation modeling), but the results are not comparable. In the GSEM, I built a model with my latent variable is the real quality of life and the observed variables are many questions of a questionnaire. The results of Cronbach´alpha are very good (>0.80) in most of domains. The results of GSEM (coeficient) are also good , but I have differences in different questions. Can I have a tool to decide what is better?
Hi Claudia,
I was intrigued bt=y your question and took a liitle time to understand it in my own way. A summary of my conclusion follows.
Chronbach alpha is a dimensionless number between zero and 1 that measures consistency between the items. It measures of how closely the n (discrete) items in a group are related to the group in terms of ratio of covariances and variances of the items. It is not a statistical formula in the sense of having a distribution; it is however sensitive to outliers and non-normally distributed data. Moreover, the value of the coefficient increases as the number of items (n) in the equation increases. Note that alpha can be numerically < 0 (negative) and also > 1 depending on the magnitude of the variances in the numerator and denominator. Please see https://stats.idre.ucla.edu/spss/library/how-negative-reliability-coefficients-can-occur/. If you study the equation for alpha, you might note that the scale of measurement for the items used can be studied as well. You can also study the eigen values and vectors of the variance-covariance matrix. Regarding GSEM I view it as modeling cause and effect in the presence of latent and observed variables (endogenous and endogenous). Those variables are linked in ways that imply understanding the theoretical reasons for the paths between the variables (e.g., using correlations) noting that correlations are not equivalent to causation. At best, they are association that may be considered causal, in the sense of an equilibrium between the variables (the structure of the relationships is at equilibrium with the rest of its surroundings),=. If you go to stata.com you will find much that can inform you about SEM and GSEM.
Not sure if I helped. Good luck.
Paolo
Hi Claudia,
I was intrigued bt=y your question and took a liitle time to understand it in my own way. A summary of my conclusion follows.
Chronbach alpha is a dimensionless number between zero and 1 that measures consistency between the items. It measures of how closely the n (discrete) items in a group are related to the group in terms of ratio of covariances and variances of the items. It is not a statistical formula in the sense of having a distribution; it is however sensitive to outliers and non-normally distributed data. Moreover, the value of the coefficient increases as the number of items (n) in the equation increases. Note that alpha can be numerically < 0 (negative) and also > 1 depending on the magnitude of the variances in the numerator and denominator. Please see https://stats.idre.ucla.edu/spss/library/how-negative-reliability-coefficients-can-occur/. If you study the equation for alpha, you might note that the scale of measurement for the items used can be studied as well. You can also study the eigen values and vectors of the variance-covariance matrix. Regarding GSEM I view it as modeling cause and effect in the presence of latent and observed variables (endogenous and endogenous). Those variables are linked in ways that imply understanding the theoretical reasons for the paths between the variables (e.g., using correlations) noting that correlations are not equivalent to causation. At best, they are association that may be considered causal, in the sense of an equilibrium between the variables (the structure of the relationships is at equilibrium with the rest of its surroundings),=. If you go to stata.com you will find much that can inform you about SEM and GSEM.
Not sure if I helped. Good luck.
Paolo
Cronbach's alpha is already a good method of estimating the reliability of a research instrument and its subscales. However, if you want to determine more precisely the reliability and validity. especially construct validity of the whole instrument as well as the subscales, you may further validate your instrument using factor analysis.
I applaud and recommend Paolo F Ricci 's comprehensive answer! Statistics are useful guides for decisions, but cannot replace (or even justify) the required decisions themselves. The nature of life is that we are NEVER 'certain' of anything. ;)
Cheers,
Steven
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