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It looks like factanal is unable to optimize from these starting values
(kinda like the error message says). So, factanal.fit.mle isn't converging
and you have problems with your analysis. Try putting control = list(trace =
T) in your code to see what happenens. E.g.,

R >
R >      v1 <- c(1,1,1,1,1,1,1,1,1,1,3,3,3,3,3,4,5,6)
R >      v2 <- c(1,2,1,1,1,1,2,1,2,1,3,4,3,3,3,4,6,5)
R >      v3 <- c(3,3,3,3,3,1,1,1,1,1,1,1,1,1,1,5,4,6)
R >      v4 <- c(3,3,4,3,3,1,1,2,1,1,1,1,2,1,1,5,6,4)
R >      v5 <- c(1,1,1,1,1,3,3,3,3,3,1,1,1,1,1,6,4,5)
R >      v6 <- c(1,1,1,2,1,3,3,3,4,3,1,1,1,2,1,6,5,4)
R >      m1 <- cbind(v1,v2,v3,v4,v5,v6)
R >      factanal(m1, factors=3, control = list(trace = T))
start 1 value: 0.4755156 uniqs: 0.0050 0.1009 0.0050 0.2241 0.0843 0.0050

Call:
factanal(x = m1, factors = 3, control = list(trace = T))

Uniquenesses:
   v1    v2    v3    v4    v5    v6
0.005 0.101 0.005 0.224 0.084 0.005

Loadings:
   Factor1 Factor2 Factor3
v1 0.944   0.182   0.267
v2 0.905   0.235   0.159
v3 0.236   0.210   0.946
v4 0.180   0.242   0.828
v5 0.242   0.881   0.286
v6 0.193   0.959   0.196

               Factor1 Factor2 Factor3
SS loadings      1.893   1.886   1.797
Proportion Var   0.316   0.314   0.300
Cumulative Var   0.316   0.630   0.929

The degrees of freedom for the model is 0 and the fit was 0.4755
R >

If you think the model should be OK and there isn't an error somewhere else
then you'll want to fiddle with the control options. From the help for
fractanal:

 control: A list of control values,

          nstart The number of starting values to be tried if 'start =
               NULL'. Default 1.

          trace logical. Output tracing information? Default 'FALSE'.

          lower The lower bound for uniquenesses during optimization.
               Should be > 0. Default 0.005.

          opt A list of control values to be passed to 'optim''s
               'control' argument.

          rotate a list of additional arguments for the rotation
               function.

     ...: Components of 'control' can also be supplied as named
          arguments to 'factanal'.


HTH, Andy
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