Variables:
Details
Holzinger and Swineford (1937) introduced the bifactor model (one general factor and several group factors) for mental abilities. This is a nice demonstration data set of a hierarchical factor structure that can be analyzed using the omega function or using sem. The bifactor model is typically used in measures of cognitive ability.
There are several ways to analyze such data. One is to use the omega function to do a hierarchical factoring using the Schmid-Leiman transformation. This can then be done as an exploratory and then as a confirmatory model using omegaSem. Another way is to do a regular factor analysis and use either a bifactor or biquartimin rotation. These latter two functions implement the Jennrich and Bentler (2011) bifactor and biquartimin transformations. The bifactor rotation suffers from the problem of local minima (Mansolf and Reise, 2016) and thus a mixture of exploratory and confirmatory analysis might be preferred.
The 14 variables are ordered to reflect 3 spatial tests, 3 mental speed tests, 4 motor speed tests, and 4 verbal tests. The sample size is 355.
Another data set from Holzinger (Holzinger.9) represents 9 cognitive abilities (Holzinger, 1939) and is used as an example by Karl Joreskog (2003) for factor analysis by the MINRES algorithm and also appears in the LISREL manual as example NPV.KM.
Another classic data set is the 9 variable Thurstone problem which is discussed in detail by R. P. McDonald (1985, 1999) and and is used as example in the sem package as well as in the PROC CALIS manual for SAS. These nine tests were grouped by Thurstone and Thurstone, 1941 (based on other data) into three factors: Verbal Comprehension, Word Fluency, and Reasoning. The original data came from Thurstone and Thurstone (1941) but were reanalyzed by Bechthold (1961) who broke the data set into two. McDonald, in turn, selected these nine variables from the larger set of 17 found in Bechtoldt.2. The sample size is 213.
Another set of 9 cognitive variables attributed to Thurstone (1933) is the data set of 4,175 students reported by Professor Brigham of Princeton to the College Entrance Examination Board. This set does not show a clear bifactor solution but is included as a demonstration of the differences between a maximimum likelihood factor analysis solution versus a principal axis factor solution.
Tucker (1958) uses 9 variables from Thurstone and Thburstone (1941) for his example of interbattery factor analysis.
More recent applications of the bifactor model are to the measurement of psychological status. The Reise data set is a correlation matrix based upon >35,000 observations to the Consumer Assessment of Health Care Provideers and Systems survey instrument. Reise, Morizot, and Hays (2007) describe a bifactor solution based upon 1,000 cases.
The five factors from Reise et al. reflect Getting care quickly (1-3), Doctor communicates well (4-7), Courteous and helpful staff (8,9), Getting needed care (10-13), and Health plan customer service (14-16).
The two Bechtoldt data sets are two samples from Thurstone and Thurstone (1941). They include 17 variables, 9 of which were used by McDonald to form the Thurstone data set. The sample sizes are 212 and 213 respectively. The six proposed factors reflect memory, verbal, words, space, number and reasoning with three markers for all expect the rote memory factor. 9 variables from this set appear in the Thurstone data set.
Two more data sets with similar structures are found in the Harman data set. This includes the another 9 variables (with 696 subjects) from Holzinger used by Harman link{Harman.Holzinger} as well as 8 affective variables from link{burt}.
Another data set that is worth examining for tests of bifactor structure is the holzinger.swineford data set which includes the original data from Holzinger and Swineford (1939) supplied by Keith Widaman. This is in psychTools.1.9.11 or later.
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Bechtoldt.1: 17 x 17 correlation matrix of ability tests, N = 212.
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Bechtoldt.2: 17 x 17 correlation matrix of ability tests, N = 213.
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Holzinger: 14 x 14 correlation matrix of ability tests, N = 355
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Holzinger.9: 9 x 9 correlation matrix of ability tests, N = 145
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Reise: 16 x 16 correlation matrix of health satisfaction items. N = 35,000
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Thurstone: 9 x 9 correlation matrix of ability tests, N = 213
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Thurstone.33: Another 9 x 9 correlation matrix of ability items, N=4175
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Thurstone:9: And yet another 9 x 9 correlation matrix of ability items, N =710
