Previously I calculated the bunch of above 50 items by some extraordinary way and got 3 scales and now recalculating them as it should be.

Previously I used Statistica 12.0 and AMOS 23.0. Now for EFA I’m using Factor 12.03.01 64 bits (https://psico.fcep.urv.cat/utilitats/factor/Download.html).

So, concerning the number of factors:

- Hull recommends me 1 factor,

- MAP – 3 factors,

- Parallel analysis – 5 factors.

As I know from my previous exploration of these items, 3 factors for the first steps are bad interpretable and very noisy. If we take 5 factors, they are quite understandable but by step by step removing weak items will be got the structure of 3 or maybe 4 factors (scales).

So, concerning the item selection.

Factor 12.03 gives me a bunch of opportunity. But which of them should be consider as statistical criteria for selecting items and which of them are common ‘decision rules’ for selecting items and how one can prove this decision rules?

Factor 12.03. provides measurement of sample adequacy, MSA (Lorenzo-Seva & Ferrando, 2021) everywhere as such criteria. I like and appreciate this opportunity but at initially steps of selecting items it brings some risks for washing out scales with low quantity of items and for washing out some unique questions with low communalities.

I would like to use D, communality-standardized Pratt’s measure (Wu & Zumbo, 2017), as a criterion for items selection at very first steps because in considering (a) the unique contribution of a factor to an item’s observed variation (i.e. Pratt’ss measure) and (b) uniqueness of questions.

For example, I have an item V58. Factor 12.03 suggests that I remove it because of prefactor solution.

Items Normed 95% Confidence The Pool

MSA interval

----- ------------------------- --------

58 0.661 (0.493 -- 0.726) Might not work - Revise

----- ------------------------- --------

I would lice to see how V58 should be bad

So what I have found by further Factor 12.03 using.

Variable Mean Confidence Interval Variance Skewness Kurtosis

(95%) (Zero centered)

s_12_58 3.300 ( 3.21 3.39) 0.885 -0.061 0.008

Good

Variable 58

Value Freq

|

1 24 | ***

2 78 | *********

3 320 | ****************************************

4 174 | *********************

5 77 | *********

+-----------+---------+---------+-----------+

0 80.0 160.0 240.0 320.0

Almost excellent

ROTATED LOADING MATRIX

Variable F 1 F 2 F 3 F 4 F 5

s_12_58 0.160 0.257 0.002 0.065 -0.008

The loadings are low. Maybe one should exclude V58, because loadings are less than |0.300|. It is one of decision rules (but I don’t know how I can prove it). Let’s see other V58 characteristics.

UNROTATED LOADING MATRIX

Variable F 1 F 2 F 3 F 4 F 5 Communality

s_12_58 0.076 -0.233 -0.147 -0.016 -0.038 0.083

But because of low communality V58 should be unique.

It means that afterwards

COMMUNALITY-STANDARDIZED PRATT'S MEASURES

Variable F 1 F 2 F 3 F 4 F 5

s_12_58 0.161 0.771 0.000 0.064 0.004

These communality-standardized Pratt's measures for V58 look optimistic, so V58 shouldn’t be removed at least during these first steps.

And I should assess some residuals.

Largest Negative Standardized Residuals

…

Residual for Var 39 and Var 6 -2.95

Residual for Var 58 and Var 6 -2.70

…

Largest Positive Standardized Residuals

…

Residual for Var 8 and Var 6 2.65

Residual for Var 42 and Var 6 2.58

Residual for Var 52 and Var 23 2.96

Residual for Var 54 and Var 6 3.23

Residual for Var 58 and Var 28 2.63

Residual for Var 58 and Var 52 2.61

And for my sorrow bunch of Indices for detecting correlated residuals (doublets) should not work in Factor 12.03 because program calculate these indices with all excluded variables (((.

So, concerning items selection the questions are:

- If one so interested in communality-standardized Pratt's measures why can he formulate or prove the decision rule for it. Is it decision rule or statistical criterion?

- When and why should be used MSA, if it probably depends of ‘noise’ items and proportions of quantity of items in scales?

- How could one prove the cutoff of 0.300 for loadings?

- Which are decision rules for standardized residuals?

Thank you very much I’ll be happy every advice in this sphere.

Lorenzo-Seva, U., & Ferrando, P. J. (2021). MSA: The forgotten index for identifying inappropriate items before computing exploratory item factor analysis. Methodology, 17(4), Article 4. https://doi.org/10.5964/meth.7185

Wu, A., & Zumbo, B. (2017). Using Pratt’s Importance Measures in Confirmatory Factor Analyses. Journal of Modern Applied Statistical Methods, 16(2), 81–98. https://doi.org/10.22237/jmasm/1509494700