I am trying to create a plot of a logistic function with parameters AHAT and MDIF. The values of these parameters depend up underlying parameters A and DIF and an underlying ability distribution with a covariance omega and mean vector mu. I have to go through several steps to determine AHAT and MDIF. I would like to create a plot where I can manipulate sigma, mu1 and mu2 to see how it affects the logistic curve. I can't figure out how to create the plot. Leaving the variable sigma and mu1 and mu2 in the expressions at the outside will not work. I have attached a MSWord document with the code. Does any have suggestions?
A={{1.2,.4},{.8,.5},{.9,1.0},{1.3,.5},{.6,.9}};u={{?1,?2}};
DIF={{.5},{.7},{1.0},{-1.},{2.0}};
?={{?,1},{1,?}}
L=CholeskyDecomposition[?]
W=Eigenvectors[Transpose[L].Transpose[A].A.L]
AM=List[A[[1]]]
W1M=List[W[[1]]]
W2M=List[W[[2]]]
AHAT=AM.Transpose[W1M]/Sqrt[2.89+AM.Transpose[W2M].W2M.Transpose[AM]]
MDIF=(DIF[[1]]-AM.Transpose[u])/AM.Transpose[W1M]
Manipulate[Plot[{(1/(1+Exp[-1.7*AHAT*(?-MDIF)])),},{?,-3,3},AxesLabel->{?,p}],{?,1,3},{?1,-2,2},{?2,-2,2}]
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