[R] factanal results interpretation - am I right here?

[RenE J.V. Bertin]

Hi,

I have obtained some results with factanal that seem to support a hypothesis I already had, and I'd like to verify that I can indeed conclude this from this new analysis.

We had subjects reproduce perceived trajectories with a device that allowed us to measure spatial position (the path) and the device's orientation at any of those positions. From this, we calculated the rotation of the reproduced path (e.g. 180deg. for half a circle), the total yaw (total rotation of the device), and the average orientation relative to the path (e.g. 0deg for "tangential", 90deg. for inward or outward). We analysed the errors in these measures, compared to the presented values, and normalised to the total perceived amount of yaw:

yrelerr.PathRot, relerr.Yaw and relerr.PathRel.Orn

Additionally, we calculated measures of overlap (more exactly: average pointwise distance after maximising overlap): Spat for the path, Orn for the orientation; there were combined into FD=sqrt(Spat^2+Orn^2).

Earlier analysis had suggested that subjects assume a fixed orientation relative to the path, effectively coupling Yaw and PathRot (and assigning all perceived Yaw to PathRot). In the factanal results, I find that Spat and Orn are in separate factors (as might be expected a-priorily), but relerr.Yaw and yrelerr.PathRot are consistently grouped together (also when I use the non-normalised errors). Can I take this as a confirmation of the hypothesis that Yaw is attributed to a rotation of the path (PathRot)?

Thank you in advance,
RenE Bertin

Example of results:
# For modality=='VisVest':
> attach(subset(VV1bc.20020701.LY, VV1bc.20020701.LY$Modality=='VisVest') )
> VV1.factanal( cbind(yrelerr.PathRot,relerr.Yaw,relerr.PathRel.Orn,Spat,Orn,FD), factors=3)

Call:
factanal(factors = factors, covmat = cov(dmat, use = "complete.obs"),     na.action = na.omit)

Uniquenesses:
   yrelerr.PathRot         relerr.Yaw relerr.PathRel.Orn               Spat                Orn                 FD
             0.005              0.163              0.587              0.005              0.005              0.005

Loadings:
                   Factor1 Factor2 Factor3
yrelerr.PathRot     0.483   0.871
relerr.Yaw                  0.910
relerr.PathRel.Orn -0.473  -0.233   0.368
Spat                0.983   0.167
Orn                 0.168           0.982
FD                  0.949   0.147   0.271

# for Modality==Vis:
Uniquenesses:
   yrelerr.PathRot         relerr.Yaw relerr.PathRel.Orn               Spat                Orn                 FD
             0.331              0.005              0.851              0.005              0.005              0.005

Loadings:
                   Factor1 Factor2 Factor3
yrelerr.PathRot     0.469   0.669
relerr.Yaw          0.150   0.984
relerr.PathRel.Orn -0.355  -0.147
Spat                0.962   0.188  -0.189
Orn                                 0.996
FD                  0.979   0.180


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