Error running CFA with cross-loadings

[Amanda_Lemon]

Hi all, 

I am trying to run a two-factor CFA model where all items cross-load. 

proc calis data = data modification; 
lineqs
V1 = L11 F1 + L12 F2 + eV1,
V2 = L21 F1 + L22 F2 + eV2, 
V3 = L31 F1 + L32 F2 + eV3,
V4 = L41 F1 + L42 F2 + eV4, 
V5 = L51 F1 + L52 F2 + eV5, 
V6 = L61 F1 + L62 F2 + eV6, 
V7 = L71 F1 + L72 F2 + eV7, 
V8 = L81 F1 + L82 F2 + eV8,
V9 = L91 F1 + L92 F2 + eV9,
V10 = L101 + L102 F2 + eV10; 

variance 
F1 = 1, F2 = 1,  
eV1 - eV10 = vareV1 - vareV10;

var V1 - V10;
run; 

However, I get the following error message: 

"NOTE: The Moore-Penrose inverse is used in computing the covariance matrix for parameter estimates.
WARNING: Standard errors and t values might not be accurate with the use of the Moore-Penrose inverse.
WARNING: Lagrange multiplier statistics and Wald statistics might not be accurate with the use of the Moore-Penrose inverse in computing the covariance matrix for parameter estimates."

Why does it happen? 

[Rick_SAS · Accepted solution]

The Moore-Penrose inverse is a "pseudo-inverse" that enables you to find a solution to a singular system of equations. For details, see 

"Generalized inverses for matrices"

and

"Singular parameterizations, generalized inverses, and regression estimates"

Briefly, this means that your system of equations has linear dependencies. SAS is trying to provide you with a solution by using a generalized inverse. However, the inverse is used for certain inferential statistics (standard errors, confidence intervals, and p-values) so you are being warned that those computations are affected by the singular system.

These kinds of warnings often arise when you overspecify a model by including too many effects, or when one variable is a linear combination of other variables.