Interpret the varimax factors

Assignment Help Applied Statistics

Reference no: EM132283422

Exercise -

Q1. Consider the following principal components solution with five variables using no rotation and then a varimax rotation. Only the first two components are given, because the eigenvalues corresponding to the remaining components were very small (< .3).

Variables	Unrotated solution		Varimax solution
Variables	Comp 1	Comp 2	Comp 1	Comp 2
1	.581	.806	.016	.994
2	.767	-.545	.941	-.009
3	.672	.726	.137	.980
4	.932	-.104	.825	.447
5	.791	-.558	.968	-.006

(a) Find the amount and percent of variance accounted for by each unrotated component.

(b) Find the amount and percent of variance accounted for by each varimax rotated component.

(c) Compare the variance accounted for by each unrotated component with the variance accounted for by each corresponding rotated component.

(d) Compare (to 2 decimal places) the total amount and percent of variance accounted for by the two unrotated components with the total amount and percent of variance accounted for by the two rotated components. Does rotation change the variance accounted for by the two components?

(e) Compute the communality (to two decimal places) for the first observed variable using the loadings from the (i) unrotated loadings and (ii) loadings following rotation. Do communalities change with rotation?

Q2. Using the correlation matrix shown in Table 9.3, run an exploratory factor analysis (as illustrated in section 9.12) using principal axis extraction with direct quartimin rotation.

(a) Confirm that the use of Kaiser's rule (using the unreduced correlation matrix) and use of parallel analysis as discussed in sections 9.11 and 9.12 (using the reduced correlation matrix) provide support for a tewo factor solution.

(b) Do the values in the pattern matrix provide support for the two-factor solution that was obtained in section 9.7?

Q3. For additional practice in conducting an exploratory factor analysis, run an exploratory factor analysis using principal axis extraction using the correlation shown in Table 9.7 but do not include the bodily symptom items. Run a two-and three-factor solution for the remaining nine items.

(a) Which solution(s) have empirical support?

(b) Which solution seems more conceptually meaningful?

Q4. Bolton (1971) measured 159 deaf rehabilitation candidates on 10 communication skills, of which six were reception skills in unaided hearing, aided hearing, speech reading, reading, manual signs, and finger spellings. The other four communication skills were expression skills: oral speech, writing, manual signs, and finger-spelling. Bolton conducted an exploratory factor analysis using principal axis extraction with a varimax rotation. He obtained the following correlation matrix and varimax factor solution:

Correlation Matrix of Communication Variables for 159 Deaf Persons
	C₁	C₂	C₃	C₄	C₅	C₆	C₇	C₈	C₉	C₁₀	M	S
C₁	39										1.10	0.45
C₂	59	55									1.49	1.06
C₃	30	34	61								2.56	1.17
C₄	16	24	62	81							2.63	1.11
C₅	-02	-13	28	37	92						3.30	1.50
C₆	00	-05	42	51	90	94					2.90	1.44
C₇	39	61	70	59	05	20	71				2.14	1.31
C₈	17	29	57	88	30	46	60	78			2.42	1.04
C₉	-04	-14	28	33	93	86	04	25	92		3.25	1.49
C₁₀	-04	-08	42	50	87	94	17	45	90	94	2.89	1.41

Note - The italicized diagonal values are squared multiple correlations.

Varimax Factor Solutions for 10 Communication Variables for 159 Deaf Persons
		I	II
C₁	Hearing (unaided)		49
C₂	Hearing (aided)		66
C₃	Speech reading	32	70
C₄	Reading	45	71
C₅	Manual signs	94
C₆	Finger-spelling	94
C₇	Speech		86
C₈	Writing	38	72
C₉	Manual signs	34
C₁₀	Fingerspelling	96
Percent of common variance		53.8	39.3

Note: Factor loadings less than .30 are omitted.

(a) Interpret the varimax factors. What does each of them represent?

(b) Does the way the variables that define factor 1 correspond to the way they are correlated? That is, is the empirical clustering of the variables by the principal axis technique consistent with the way those variables go together in the original correlation matrix?

Q5. Consider the following part of the quote from Pedhazur and Schmelkin (1991): "It boils down to the question: Are aspects of a postulated multidimensional construct intercorrelated? The answer to this question is relegated to the status of an assumption when an orthogonal rotation is employed". What did they mean by the last part of this statement?

Note - Please answer the questions 2, 3 and 4 from exercise.

Attachment:- Assignment Files.rar

Reference no: EM132283422

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len2283422

4/15/2019 12:29:08 AM

Instructions: PLEASE ANSWER THE QUESTION 2, 3,4 FROM Exercise 9.19 as attached by following the instructions. Attached you will find the syntax from Chapter 9 and the appropriate parallel analysis syntax. To generate the parallel syntax screen plot for problem 3, be sure and change the syntax at the end to save the results and get the file.

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