scores from factor analysis

[Baoying Lin]

Hello,

I have one question, may be more of statistic question:

I could like to know V1, v2, V3, V4 and V5's impact on Cost Y. I run factor analysis on V1-v5, and then predict X as factor1 was able to explain more than 90%.(Command: factor v1-v5; prediect X). Could anyone tell me how I get X from V1-V5. I have factor loading and scoring coefficients, but I could not figure out how it get to X.

Here are the V1-v5
V1 V2 V3 V4 V5
3183 4471 8867 1425 1720
2853 4327 8327 1428 1871
2796 3897 7285 1157 1679
2570 3545 7356 1055 1604
2417 2718 5945 824 1422
2412 2909 6424 663 1518
2396 2722 6786 488 1520
2254 2661 5730 343 1381
2314 2427 5338 325 1485
2156 2899 4263 340 1448
1962 3205 3962 380 1458


And my X is
1.700504
1.514663
.8673126
.4921271
-.3481589
-.2396494
-.3608734
-.8328244
-.8243592
-.9612715
-1.007469

also if my regression function is Y=C+bX.As X is an index score, I could said by changing 1 unit of index score, Y will change b. Is it anyway I could tie back the results to V1-V5?

Many thanks.

[Richard Williams]

I suggest you type -help factor postestimation- but then click on the actual manual pdf entry. In Stata 13 a discussion starts on p. 334 of the MV manual. You could also check out the papers by Bartlett and Thomson that are cited.

[Richard Williams]

If I understand what you want to do, I think you could do

reg X V1 - V5

The correlation should be 1. Then substitute the equation for X into your formula, e.g.

Y=C+bX = C + b*(b1V1 + b2V2 + b3V3 + b4V4 + b5V5 + constant)

So if, say, b = .2 and b1 = .3, you would say that a 1 unit increase in V1 results, on average, in a .2 * .3 = .06 increase in Y

Here is an example:

use http://www3.nd.edu/~rwilliam/statafiles/anomia.dta, clear
ren anomia* v*
factor v1-v5
predict x
reg age x
predict p1
reg x v1-v5
gen p2 = 43.76367 + 1.348543 * (.4490945 * v1 +.5334469 * v2 +.6151449 * v3 + .4176787 * v4 + .4896154 * v5  -.9834715)
corr p1 p2
di "effect of v1 on age is " 1.348543 * .4490945

[Richard Williams]

To put it another way, X is a weighted sum of V1-V5. So, to get the effects of V1-V5 on Y, you regress Y on X and get the slope coefficient for X, and then multiply that slope coefficient by the weights for X (which you can get by regressing X on V1-V5).

At least I think that is what you do. This was just a quick improvisation on my part, so somebody can feel free to correct me or come up with a better solution.

[Nick Cox]

My comment is quite different. Given V1 ... V5 that influence some variable and an interest in regression, I would use regress directly. Pushing the data into factor analysis and getting scores out is unlikely to give a more useful or interesting model.

[Richard Williams]

It may depend on how good your scale is. It may not be worth it to create a scale from V1-V5, but it may be worth it to create a scale from V1-V100. And how well do the items hang together as a scale? Rather than a factor analysis you may want to set up a Structural Equation Model where v1-v5 are indicators of an underlying latent variable. Factor analysis can give you parsimony, but does that parsimony come at the loss of important information? There are many issues to consider when deciding whether or not to use factor analysis and create scales from items. But there are zillions of scales out there measuring all sorts of things; and in analyses you will often use the score on the scale rather than the score for each individual item used to compute the scale.