How to use Spearman's correlation in lavaan?
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Fabrício Fialho
Feb 2, 2023, 11:16:18 AM2/2/23
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I would appreciate your comments on the following aspect of a replication project:
The aim is to conduct a unidimensional factor analysis. The relevant variables are the rank-order of a set of 8 objects and, long story short, I would fit a CFA with these rank-order variables. (I recognize there is contention on running factor analysis with rank-order and ipsative data, and a models have been proposed for that e.g. https://doi.org/10.1177/004912418000900206 and https://doi.org/10.1007/BF02294861 etc. but this goes way beyond the aims of the project.)
The available information is just the data set with the rank-ordering where each object if ranked from 1st to 8th is carried out by respondents.
Two analyses are to be conductd in two ways:
(1) Using the complete ranking of the variables (from 1st to 8th);
(2) Using a partial/tied ranking, variables are recoded as binaries where 1=the object is in the top 4 objects (i.e., ranked 1st-4th), 0=else.
Given this scenario, I wonder whether there is a way to use Spearman's rank correlation instead of, say, polychoric correlation in lavaan.
I noticed that Polychoric correlation and Spearman's correlation return very similar results for the complete rankings however there are differences for the dichotomous variables. The Spearman's correlation for the binary variables is very similar to the results for complete ranking; when polychoric correlation is used the correlations for the binary variables are considerably stronger than Spearman's (for instance, a -0.22 correlation becomes -0.34) and I am concerned on how this could affect the results.
I hope my question is not too convoluted!
NB: lavaan support using a covariance matrix as input but it is unclear to me whether the procedure applies to correlation matrix https://lavaan.ugent.be/tutorial/tutorial.pdf
The aim is to conduct a unidimensional factor analysis. The relevant variables are the rank-order of a set of 8 objects and, long story short, I would fit a CFA with these rank-order variables. (I recognize there is contention on running factor analysis with rank-order and ipsative data, and a models have been proposed for that e.g. https://doi.org/10.1177/004912418000900206 and https://doi.org/10.1007/BF02294861 etc. but this goes way beyond the aims of the project.)
The available information is just the data set with the rank-ordering where each object if ranked from 1st to 8th is carried out by respondents.
Two analyses are to be conductd in two ways:
(1) Using the complete ranking of the variables (from 1st to 8th);
(2) Using a partial/tied ranking, variables are recoded as binaries where 1=the object is in the top 4 objects (i.e., ranked 1st-4th), 0=else.
Given this scenario, I wonder whether there is a way to use Spearman's rank correlation instead of, say, polychoric correlation in lavaan.
I noticed that Polychoric correlation and Spearman's correlation return very similar results for the complete rankings however there are differences for the dichotomous variables. The Spearman's correlation for the binary variables is very similar to the results for complete ranking; when polychoric correlation is used the correlations for the binary variables are considerably stronger than Spearman's (for instance, a -0.22 correlation becomes -0.34) and I am concerned on how this could affect the results.
I hope my question is not too convoluted!
NB: lavaan support using a covariance matrix as input but it is unclear to me whether the procedure applies to correlation matrix https://lavaan.ugent.be/tutorial/tutorial.pdf
Terrence Jorgensen
Feb 3, 2023, 9:20:46 AM2/3/23
to lavaan
lavaan will analyze whatever sample.cov= argument you provide. The SEs and tests will not be trustworthy unless your residual variances are fixed to ensure the total variance = 1 (by definition). In practice, you could label all the parameters, then constrain residual variances to == 1 minus the explained variance (which can be difficult to calculate in complex models).
Terrence D. Jorgensen
Assistant Professor, Methods and Statistics
Research Institute for Child Development and Education, the University of Amsterdam
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