Ciência normal e suas ferramentas: Revisando os efeitos dos métodos de análise fatorial exploratória em Administração

Rossoni, Luciano; Engelbert, Ricardo; Bellegard, Ney Luiz

doi:10.5700/rausp1234

Luciano Rossoni

Universidade do Grande Rio - Rio de Janeiro/RJ, Brasil

Luciano Rossoni, Professor do Programa de Pós-Graduação em Administração da Universidade Grande Rio (CEP 20021-180 - Rio de Janeiro/RJ, Brasil). E-mail: lrossoni@gmail.com Address: Universidade Grande Rio Rua da Lapa, 86 20021-180 - Rio de Janeiro, RJ - Brasil

Ricardo Engelbert

ISE Business School - São Paulo/SP, Brasil

Ricardo Engelbert, Professor do ISE Business School (CEP 01321-001 - São Paulo/SP, Brasil). E-mail: ricardo@engelbert.com.br

Ney Luiz Bellegard

Universidade Positivo - Curitiba/PR, Brasil

Ney Luiz Bellegard, Doutor em Administração pela Universidade Positivo (CEP 80250 060 - Curitiba/PR, Brasil), Consultor de Empresas. E-mail: neybellegard@gvmail.br

Luciano Rossoni, Professor do Programa de Pós-Graduação em Administração da Universidade Grande Rio (CEP 20021-180 - Rio de Janeiro/RJ, Brasil). E-mail: lrossoni@gmail.com Address: Universidade Grande Rio Rua da Lapa, 86 20021-180 - Rio de Janeiro, RJ - Brasil

Ricardo Engelbert, Professor do ISE Business School (CEP 01321-001 - São Paulo/SP, Brasil). E-mail: ricardo@engelbert.com.br

Ney Luiz Bellegard, Doutor em Administração pela Universidade Positivo (CEP 80250 060 - Curitiba/PR, Brasil), Consultor de Empresas. E-mail: neybellegard@gvmail.br

	Minimum	Maximum	Average
Cases	22	1025	306
Variables	3	69	28
Cases per variable	2	27	13
Scalar amplitude	4	11	6
Kaiser-Meyer-Olkin (KMO)	0.566	0.971	0.804
Total Explained Variance (%)
Principal Components, Eigenvalue^* * Significant difference when compared to the other methods (p < 0.001 in Sidak’s post hoc test).	47.3	73.8	62.4
Principal Axis Factoring, Eigenvalue	35.1	63.0	50.7
Maximum Likelihood, Eigenvalue	35.6	63.1	50.8
Principal Components, Scree Plot^* * Significant difference when compared to the other methods (p < 0.001 in Sidak’s post hoc test).	30.6	67.8	48.2
Principal Axis Factoring. Scree Plot	26.6	56.6	40.5
Maximum Likelihood, Scree Plot	26.5	56.4	40.5

Comparison of the Methods	Average	Correlation (Spearman's rho)
Comparison of the Methods	Average	Cases	Variables	Cases per Variable	Scale	KMO	Eigenvalue Factors	Scree Factors
Extraction by Eigenvalue
Principal Components vs. Principal Axis Factoring	76%	0.126	-0.180	0.329	0.145	0.357	-0.304	-0.266
Principal Components vs. Maximum Likelihood	73%	0.044	-0.271	0.282	0.150	0.235	-0.390	-0.388
Principal Axis Factoring vs. Maximum Likelihood	74%	0.035	-0.386	0.292	0.081	0.085	-0.381	-0.068
Extraction by Scree Plot
Principal Components vs. Principal Axis Factoring	79%	0.334	-0.445^* * Correlation is significant at the 0.05 level (1-tailed).	0.707^ Correlation is significant at the 0.01 level (1-tailed).	-0.201	0.302	-0.676^ Correlation is significant at the 0.01 level (1-tailed).	-0.092
Principal Components vs. Maximum Likelihood	65%	0.120	-0.485^* * Correlation is significant at the 0.05 level (1-tailed).	0.589^ Correlation is significant at the 0.01 level (1-tailed).	-0.051	0.332	-0.720^ Correlation is significant at the 0.01 level (1-tailed).	-0.240
Principal Axis Factoring vs. Maximum Likelihood	65%	0.196	-0.428^* * Correlation is significant at the 0.05 level (1-tailed).	0.593^ Correlation is significant at the 0.01 level (1-tailed).	-0.063	0.392	-0.665^ Correlation is significant at the 0.01 level (1-tailed).	-0.150
Rotation by Scree Plot
Varimax vs. Quartimax	83%	0.044	-0.798^ Correlation is significant at the 0.01 level (1-tailed).	0.610^ Correlation is significant at the 0.01 level (1-tailed).	-0.170	-0.105	-0.798^ Correlation is significant at the 0.01 level (1-tailed).	-0.198
Varimax vs. Direct Oblimin	81%	0.098	-0.569^ Correlation is significant at the 0.01 level (1-tailed).	0.469^* * Correlation is significant at the 0.05 level (1-tailed).	-0.279	-0.050	-0.504^* * Correlation is significant at the 0.05 level (1-tailed).	-0.252
Quartimax vs. Direct Oblimin	84%	0.386	-0.337	0.639^ Correlation is significant at the 0.01 level (1-tailed).	-0.248	0.170	-0.429^* * Correlation is significant at the 0.05 level (1-tailed).	-0.067

Extraction, Rotation	Cronbach (Alpha)	ICC	Pearson's r
1. Principal Axis Factoring, Varimax	0.795	0.412	0.440
2. Maximum Likelihood, Varimax	0.803	0.435	0.445
3. Principal Components, Varimax	0.780	0.367	0.430
4. Principal Components, Quartimax	0.758	0.363	0.374
5. Principal Components, Direct Oblimin	0.774	0.355	0.429

Extraction and Rotaion Methods	Cases	Variables	Cases per Variable	Scale	KMO
Cronbach's Alpha
1. Principal Axis Factoring, Varimax	0.322	-0.433^* * Correlation is significant at the 0.05 level (1-tailed); Spearman’s rho.	-0.072	0.098	0.750^ Correlation is significant at the 0.01 level (1-tailed).
2. Maximum Likelihood, Varimax	0.270	-0.525^ Correlation is significant at the 0.01 level (1-tailed).	-0.050	0.198	0.683^ Correlation is significant at the 0.01 level (1-tailed).
3. Principal Components, Varimax	0.247	-0.489^* * Correlation is significant at the 0.05 level (1-tailed); Spearman’s rho.	-0.029	0.186	0.697^ Correlation is significant at the 0.01 level (1-tailed).
4. Principal Components, Quartimax	0.430^* * Correlation is significant at the 0.05 level (1-tailed); Spearman’s rho.	-0.409^* * Correlation is significant at the 0.05 level (1-tailed); Spearman’s rho.	-0.177	0.222	0.747^ Correlation is significant at the 0.01 level (1-tailed).
5. Principal Components, Direct Oblimin	0.282	-0.505^ Correlation is significant at the 0.01 level (1-tailed).	-0.002	0.166	0.704^ Correlation is significant at the 0.01 level (1-tailed).
Intraclass Correlation (ICC)
1. Principal Axis Factoring, Varimax	0.093	-0.629^ Correlation is significant at the 0.01 level (1-tailed).	-0.574^ Correlation is significant at the 0.01 level (1-tailed).	0.036	0.223
2. Maximum Likelihood, Varimax	0.164	-0.341	-0.365^* * Correlation is significant at the 0.05 level (1-tailed); Spearman’s rho.	0.213	0.312
3. Principal Components, Varimax	0.238	-0.268	-0.484^* * Correlation is significant at the 0.05 level (1-tailed); Spearman’s rho.	0.069	0.563^ Correlation is significant at the 0.01 level (1-tailed).
4. Principal Components, Quartimax	0.300	-0.319	-0.524^ Correlation is significant at the 0.01 level (1-tailed).	0.157	0.561^ Correlation is significant at the 0.01 level (1-tailed).
5. Principal Components, Direct Oblimin	0.184	-0.287	-0.457^* * Correlation is significant at the 0.05 level (1-tailed); Spearman’s rho.	0.146	0.577^ Correlation is significant at the 0.01 level (1-tailed).
Pearson's Correlation Between Factors
1. Principal Axis Factoring, Varimax	0.188	-0.222	-0.135	-0.044	0.663^ Correlation is significant at the 0.01 level (1-tailed).
2. Maximum Likelihood, Varimax	0.244	-0.195	-0.194	-0.028	0.744^ Correlation is significant at the 0.01 level (1-tailed).
3. Principal Components, Varimax	0.247	-0.224	-0.198	-0.077	0.748^ Correlation is significant at the 0.01 level (1-tailed).
4. Principal Components, Quartimax	0.151	-0.075	-0.214	-0.109	0.706^ Correlation is significant at the 0.01 level (1-tailed).
5. Principal Components, Direct Oblimin	0.166	-0.219	-0.036	-0.149	0.743^ Correlation is significant at the 0.01 level (1-tailed).

Research Question		Results
1)	Do the number of cases, the number of variables, the number of cases per variable, and the scalar amplitude interfere in the EFA adjustment?	a) The significance of Bartlett's sphericity test did not vary. b) The Kaiser-Meyer--Olkin (KMO) test was very sensitive to sample size and moderately related to the number of variables and the proportion of cases per variable. There is no influence from scalar amplitude.
2)	Does the number of factors vary when we use different extraction methods?	No. Regardless of the extraction method, the number of factors is the same, using both the Eigenvalue and Scree Plot methods.
3)	Which extraction methods have the greatest total explained variance?	The extraction method by principal components has a greater total explained variance than the other methods.
4)	Do the construct variables converge on the same factor when different extraction methods are used?	No. While most of the variables converged on the same factor, some converged on different factors. However, those that tend to converge less are the ones with a smaller factor loading (between 0.4 and 0.59).
5)	Does the use of different rotation methods really define the variables in different dimensions?	Yes. Despite the vast majority of the variables fitting the same factor, a small part converged on other factors. This small part is exactly that formed by variables with a low factor loading.
6)	Does the choice of one extraction method over another affect the values of Cronbach's alpha and the ICC, generating more or less reliable factors?	We found no strong evidence that any great influence is exercised by the extraction method on reliability, despite the fact that ICC indicated that the principal components method was less reliable.
7)	Does the use of different rotation methods have an influence on the reliability measures?	No. The rotation method has little influence on reliability, despite the fact that the Varimax method showed itself to be a little more reliable by way of the ICC.
8)	Do different extraction and rotation methods affect factor discrimination?	The use of different extraction methods does not affect discrimination, but of the rotation methods, Quartimax was the one that discriminated most.
9)	Does the number of cases, the number of variables, the number of cases per variable, and scalar amplitude affect the reliability and correlation of the factors?	The value of Cronbach's alpha is associated with the value of the Kaiser-Meyer- -Olkin (KMO), even more than the number of variables. The value of the intraclass correlation (ICC) tends to rise with the increase in the proportion of cases per variable; specifically, when the principal components extraction method is used there is influence from the KMO on the ICC. Discrimination falls with the increase in the KMO, since there is an increase in the correlation between factors.

[1] Luciano Rossoni, Professor do Programa de Pós-Graduação em Administração da Universidade Grande Rio (CEP 20021-180 - Rio de Janeiro/RJ, Brasil). E-mail: lrossoni@gmail.com Address: Universidade Grande Rio Rua da Lapa, 86 20021-180 - Rio de Janeiro, RJ - Brasil

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Ciência normal e suas ferramentas: Revisando os efeitos dos métodos de análise fatorial exploratória em Administração

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