Factor analysis: values of raw component covariance matrix

[luisp]

Hello all,

I've been asked to find which theories (6 in total) have a higher "weight" for 200 participants which answered a question composed of 20 items in a questionnaire. Items that refer to the same theory are supposed to be related between them. I've selected factor analysis with principal component method for extraction and covariance matrix without rotation. Theories are acting as “latent variables” (they can't be directly observed) but, instead, they are inferred through the items of the question X in the questionnaire, acting as “observed variables". The results are:

1st: Social Norms (59,35% of variance explained)
2nd: Political Regime (53,66% of variance explained)
3rd: Social Movement (43,98% of variance explained)
4th: Relative Deprivation (35,95% of variance explained)
5th: Rational Choice (29,37% of variance explained)
Contagion Theory can’t be measured (only 1 item)

I also got the values of raw component covariance matrix (and, for all cases, between .615 and 1.433). How can I interpret the values? Or should I rely only in % of variance explained for each latent variable?

Is there any other possibility in order to know which are the most important theories (latent variables)? Thanks in advance.

Luis

[Maguin, Eugene]

I'm mostly confused by what you have done and are asking. You have six theories. Were there 20 questions for each theory (a total of 120) or were the same 20 questions used for all six theories? What do you mean by "weight"? What would I look at on the output to assess weight? I think there are more questions to ask but please begin with these.
Gene Maguin


-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of luisp
Sent: Wednesday, October 12, 2016 3:45 AM
To: [hidden email]
Subject: Factor analysis: values of raw component covariance matrix

Hello all,

I've been asked to find which theories (6 in total) have a higher "weight"
for 200 participants which answered a question composed of 20 items in a questionnaire. Items that refer to the same theory are supposed to be related between them. I've selected factor analysis with principal component method for extraction and covariance matrix without rotation. Theories are acting as “latent variables” (they can't be directly observed) but, instead, they are inferred through the items of the question X in the questionnaire, acting as “observed variables". The results are:

1st: Social Norms (59,35% of variance explained)
2nd: Political Regime (53,66% of variance explained)
3rd: Social Movement (43,98% of variance explained)
4th: Relative Deprivation (35,95% of variance explained)
5th: Rational Choice (29,37% of variance explained) Contagion Theory can’t be measured (only 1 item)

I also got the values of raw component covariance matrix (and, for all cases, between .615 and 1.433). How can I interpret the values? Or should I rely only in % of variance explained for each latent variable?

Is there any other possibility in order to know which are the most important theories (latent variables)? Thanks in advance.

Luis



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[Bruce Weaver]

I was also confused.  But based on my (quite possibly incorrect) understanding of what the OP is trying to do, I think confirmatory factor analysis (CFA) would be more appropriate, with model fits being compared via AIC or BIC, perhaps.  But of course, SPSS-Statistics has no means of carrying out CFA.

Maguin, Eugene wrote

I'm mostly confused by what you have done and are asking. You have six theories. Were there 20 questions for each theory (a total of 120) or were the same 20 questions used for all six theories? What do you mean by "weight"? What would I look at on the output to assess weight? I think there are more questions to ask but please begin with these.
Gene Maguin

--- snip the original post ---

[Jon Peck]

AMOS

On Wed, Oct 12, 2016 at 7:42 AM, Bruce Weaver <[hidden email]> wrote:

I was also confused.  But based on my (quite possibly incorrect)
understanding of what the OP is trying to do, I think confirmatory factor
analysis (CFA) would be more appropriate, with model fits being compared via
AIC or BIC, perhaps.  But of course, SPSS-Statistics has no means of
carrying out CFA.


Maguin, Eugene wrote
> I'm mostly confused by what you have done and are asking. You have six
> theories. Were there 20 questions for each theory (a total of 120) or were
> the same 20 questions used for all six theories? What do you mean by
> "weight"? What would I look at on the output to assess weight? I think
> there are more questions to ask but please begin with these.
> Gene Maguin
>
> --- snip the original post ---





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"When all else fails, RTFM."

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[luisp]

Thanks to all for your reply. I don't have AMOS (just R + Lavaan) but my main goal with this analysis is to show which are the main theories (latent variables), relying on the FA.
I did the analysis with SPSS version 24 for Mac OS. Next you can see the results for Rational Choice Theory (13 items).
In total, there are 22 items (some of them are shared between different theories).

Total Variance ExplainedTotal Variance Explained

	Component	Initial Eigenvaluesa			Extraction Sums of Squared Loadings
		Total	% of Variance	Cumulative %	Total	% of Variance	Cumulative %
Raw	1	9,388	29,374	29,374	9,388	29,374	29,374
	2	5,295	16,567	45,941	5,295	16,567	45,941
	3	2,705	8,465	54,406	2,705	8,465	54,406
	4	2,532	7,923	62,329	2,532	7,923	62,329
	5	1,969	6,161	68,489
	6	1,707	5,341	73,831
	7	1,514	4,737	78,568
	8	1,481	4,633	83,201
	9	1,293	4,047	87,248
	10	1,194	3,737	90,985
	11	1,121	3,507	94,493
	12	,975	3,050	97,543
	13	,785	2,457	100,000
Rescaled	1	9,388	29,374	29,374	3,788	29,136	29,136
	2	5,295	16,567	45,941	2,088	16,065	45,201
	3	2,705	8,465	54,406	1,120	8,613	53,814
	4	2,532	7,923	62,329	1,037	7,980	61,794
	5	1,969	6,161	68,489
	6	1,707	5,341	73,831
	7	1,514	4,737	78,568
	8	1,481	4,633	83,201
	9	1,293	4,047	87,248
	10	1,194	3,737	90,985
	11	1,121	3,507	94,493
	12	,975	3,050	97,543
	13	,785	2,457	100,000
Extraction Method: Principal Component Analysis.
a. When analyzing a covariance matrix, the initial eigenvalues are the same across the raw and rescaled solution.

Component Matrix^aComponent Matrix

	Raw				Rescaled
	Component				Component
	1	2	3	4	1	2	3	4
8.1 The duty to help others	,900	-,931	,063	-,367	,535	-,553	,038	-,218
8.2 The need to fight against injustice	,957	-,937	,419	-,025	,575	-,563	,252	-,015
8.3 Gaining recognition and respect	1,127	-,003	-,258	,086	,723	-,002	-,166	,055
8.4 Seeking for a feeling of belonging	1,231	-,267	-,183	,336	,763	-,166	-,114	,209
8.5 Feeling of liberation or rebelliousness against one’s personal situation	,989	,164	-,497	,387	,636	,105	-,319	,249
8.6 Opinions and views of important people in his/her life	,810	,214	-,837	-,335	,520	,137	-,537	-,215
8.7 Impossibility of meeting one’s expectations in life	,742	,586	-,504	-,271	,504	,397	-,342	-,184
8.9 Chance of improving life conditions (better job, better salary, access to services,…)	,609	,993	,368	-,604	,394	,642	,238	-,391
8.10 Lack of alternatives in my city or need to migrate because of that	,712	,953	,527	-,587	,436	,584	,323	-,360
8.14 Searching for love or husband/wife	,534	,596	,625	,669	,350	,391	,410	,439
8.18 To exert change in society	,790	-,548	,618	-,205	,513	-,356	,402	-,133
8.21 The feeling that one’s religious interpretation is superior to others	,792	-,276	,135	,094	,539	-,188	,092	,064
8.22 Threats or fear of suffering retaliation against himself/herself or their loved ones	,525	,662	,141	,856	,338	,427	,091	,552
Extraction Method: Principal Component Analysis.
a. 4 components extracted.