Have to use 4 factors, but EFA suggests only 2 factors

[fazzmo]

Hey,

I am trying to run a regression which takes four institutional dimensions (fixed) of a country into account.
These four dimensions are represented by four independent latent variables. I managed to find pretty good variables which reflect each of the dimensions (in theory), so that I have 4 variables per dimension, so 16 in total. However, an exploratory factor analysis points to only 2 factors, and a confirmatory factor analysis with the above-mentioned 4 factors gives me a pretty poor fit. Indeed, factors 1 and 4 have a high covariance (0.95) and factor 2 and 3 also have a pretty high covariance (0.89).

If I proceed regardless of this poor fit, do you think it is possible to draw proper conclusions from my regression? In theory, the variables measure things that fit to the respective dimensions very well.

Thank you so much.

[Rich Ulrich]

If these highly correlated factors were scores on rating scales
about people, I would figure that there were only two "real" latent
scales, and don't try too hard to find four.  But you say that these
are "institutional dimensions ... of a country." 

Well, I don't know what that includes.  But I do know that a lot of
people screw up badly on "country" data, in a few ordinary ways
that also may mess up the apparent dimensionality.

For instance, if a bunch of the numbers differ because of
population size or national area or total national wealth when those
aspects are supposed to be irrelevant... then the numerical covariances
of measuring this bosh might swamp the intended latent variables.

For instance, "per-capita income" is usually more interesting when
comparing countries than "gross domestic product". 

On the other hand, if your variables *are*  well chosen and well-measured,
then you probably don't have 4 factors.  - When two "things" are correlated
0.95, I tend to want to look at something that reflects the difference between
them.  Sometimes that is their ratio (or log of the ratio) and sometimes that
is some version of an arithmetic difference, like (mean1/SD1  - mean2/SD2) .

--
Rich Ulrich

> Date: Fri, 7 Dec 2012 11:03:42 -0800

> From: [hidden email]
> Subject: Have to use 4 factors, but EFA suggests only 2 factors
> To: [hidden email]
>
> Hey,
>
> I am trying to run a regression which takes four institutional dimensions
> (fixed) of a country into account.
> These four dimensions represent four independent latent variables. I managed
> to find pretty good variables which reflect each of the dimensions (in
> theory), so that I have 4 variables per dimension, so 16 in total. However,
> an exploratory factor analysis points to only 2 factors, and a confirmatory
> factor analysis with the above-mentioned 4 factors gives me a pretty poor
> fit. Indeed, factors 1 and 4 are highly correlated (0.95) and factor 2 and 3
> are also highly correlated (0.89).
>
> If I proceed regardless of this poor fit, do you think it is possible to
> draw proper conclusions from my regression? In theory, the variables measure
> things that fit to the respective dimensions very well.
>
> Thank you so much.
> ...

[fazzmo]

Thanks a lot. I totally agree with you.

Unfortunately I can't  change the number of dimensions, and unfortunately I can't find other variables that describe these dimensions. I am just concerned about the validity of the results.

I thought that the implication was that if dimension1 is positively and significantly related to a certain dependent variable, this implies that  dimension4, which covaries highly with dimension1, is also very likely to have a significant and positive effect on this dependent variable, right?

But when I test it, dimension 1 has a positive effect on the dependent variable, and dimension4 has a negative effect on the dependent variable. How can that be?

[Art Kendall]

Please describe your analysis in more detail.
What constitute a case?  How were they selected? are these all 200 or so countries?
What variables did you use?  How were they selected?

What are your 4 institutional dimensions? How were they measured?  over what set of countries was it determined to be 4 dimensions?
On 12/8/2012 9:05 AM, fazzmo wrote:

Thanks a lot. I totally agree with you.

Unfortunately I can't  change the number of dimensions, and unfortunately I
can't find other variables that describe these dimensions. I am just
concerned about the validity of the results.

Implication If dimension1 is positively and significantly related to a
certain dependent variable, this implies that  dimension4, which was highly
positively correlated to dimension1, is also very likely to have a
significant and positive effect on this dependent variable, right?



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[fazzmo]

Hi,

this is my problem in detail.

In my research I would like to outline that 4 institutional dimensions (regulatory, cognitive, normative, conducive) influence entrepreneurial activity of a country. The regulatory, cognitive and normative dimensions were found to be empirically distinct by Scott (1995) and have been widely ever since. The conducive dimension is based on an additional paper which I read. The idea is that promoting certain dimensions may be more important to trigger entrepreneurial activity than others.

I used the following variables for each dimension:
1. Regulatory (4 variables)
(Ease of Doing Business, Business Freedom, Property Rights Protection, Corruption Index)
2. Cognitive (3 variables)
(Perceived Capabilities to set up a business, Perceived opportunities to set up a business, Whether or not a person knows an entrepreneur)
3. Normative (3 variables)
Status attributed to entrepreneurship, MediaAttention of Entrepreneurs, Entrepreneurship as a desirable career choice)
4. Conducive (4 variables)
Availability of venture capital, Latest Technology available in a country,University-Industry collaboration,Availability of Science Engineers

The data for these variables can be drawn from several databases per country, some of them are based on large surveys. I chose these variables, because they reflect the theory about these four institutional dimensions as introduced by previous scholars perfectly. I am assuming that the 4 dimensions are found in every country.

Now, I have data for 42 countries (spread all over the world, but mostly more developed countries) over 7 years. I basically included every country for which I could find data for these variables over 7 years.

[Rich Ulrich]

Since you don't give any hint at what the dimensions are,
we don't have any new clue at what else (beyond my initial
suggestions) might be possible. 

If V1 is correlated 0.95 with V4, then V4 will have a fairly similar
correlation, guaranteed by the math, with anything that  V1 is used
to "predict".  However, if you put them both in the same regression
equation, you might see (a) the predictive weight split between the
two (maybe, with neither adding "significantly" to the other); or  (b)
two regression weights that are large and in the opposite directions. 

If you get case (a), your results are apt to be valid and somewhat
interpretable, especially when your interpretation includes strong
reference to the zero-order relationship, in addition to the regression
result.

Case (b) is called a "suppressor relationship."  Occasionally, these
are "valid" in the sense of being replicable and robust.  But if your
measurements are not known to be good scales of their own latent
dimensions, case (b) is a warning that you should do better modeling. 

--
Rich Ulrich

> Date: Sat, 8 Dec 2012 06:05:20 -0800

> From: [hidden email]
> Subject: Re: Have to use 4 factors, but EFA suggests only 2 factors
> To: [hidden email]
>
> Thanks a lot. I totally agree with you.
>
> Unfortunately I can't change the number of dimensions, and unfortunately I
> can't find other variables that describe these dimensions. I am just
> concerned about the validity of the results.
>
> Implication If dimension1 is positively and significantly related to a
> certain dependent variable, this implies that dimension4, which was highly
> positively correlated to dimension1, is also very likely to have a
> significant and positive effect on this dependent variable, right?
>
> ...

[Art Kendall]

How are you measuring entrepreneurial activity?

Was your DV fine-grained enough so that you can see any trends.
Did you look at parallel coordinate plots with the repeats as as separate variables?

Do you think that there would be a correlation between whether there is data available for 7 years and the independent variables?
Would countries that are developed be what the original work was based on? Are the IV's measured once or 7 times?

Are you summing the items on the scales?  Or are your using factor scores? Or ...?

What was your data layout for the EFA? 42 cases by 16 variables? 
When you did the EFA what did you use as a stopping rule?
Did you try parallel analysis?  How did the eigenvalues from parallel analysis  look on a scree plot of those from the EFA?

for the repeated measures did you use GLM to do the regression?

On 12/10/2012 5:06 PM, fazzmo wrote:

Hi,

this is my problem in detail.

In my research I would like to outline that 4 institutional dimensions
(regulatory, cognitive, normative, conducive) influence entrepreneurial
activity of a country. The regulatory, cognitive and normative dimensions
were found to be empirically distinct by Scott (1995) and have been widely
ever since. The conducive dimension is based on an additional paper which I
read. The idea is that promoting certain dimensions may be more important to
trigger entrepreneurial activity than others.

I used the following variables for each dimension:
/1. Regulatory (4 variables)/
(Ease of Doing Business, Business Freedom, Property Rights Protection,
Corruption Index)
/2. Cognitive (3 variables)/
(Perceived Capabilities to set up a business, Perceived opportunities to set
up a business, Whether or not a person knows an entrepreneur)
/3. Normative (3 variables)/
Status attributed to entrepreneurship, MediaAttention of Entrepreneurs,
Entrepreneurship as a desirable career choice)
/4. Conducive (4 variables)/
Availability of venture capital, Latest Technology available in a
country,University-Industry collaboration,Availability of Science Engineers

The data for these variables can be drawn from several databases per
country, some of them are based on large surveys. I chose these variables,
because they reflect the theory about these four institutional dimensions as
introduced by previous scholars perfectly. I am assuming that the 4
dimensions are found in every country.

Now, I have data for 42 countries (spread all over the world, but mostly
more developed countries) over 7 years. I basically included every country
for which I could find data for these variables over 7 years.





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