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From |
May Boggess <mboggess@stata.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: predict stdp after logistic regression; |

Date |
27 Apr 2004 10:35:58 -0500 |

On Tuesday, Gerben asked: > Who can tell me what the formula is that Stata uses for the > calculation of stdp after logistic regression? > I was unable to find it in the manuals and in the Statalist archives. After -logistic-, -predict- with the option -stdp- is calculating the standard error of the linear predictor, -xb-. Given the covariate settings (values of the independent variables, the x's) in a particular observation, the linear predictor for that observation is a function of the coefficients (the b's) of the model. So we use the delta method to calculate its standard error. This means pre and post multiplying the covariance matrix e(V) by the first derivatives (with respect to the b's) of the linear predictor. Let's look at an example: clear sysuse auto keep for turn logistic for turn, coef matrix V = e(V) predict xb,xb predict stdp,stdp list xb stdp in 1/5 For our example, the linear predictor xb is: f = b0 + b1*turn so the derivatives with repect to the b's are: df/db1 = turn df/db0 = 1 So the matrix we are going to multiply the covariance matricx e(V) by should be a 2 X 1, with the value of turn in the first component and 1 in the second. (I know what order to put them in - it has to be the same order as the columns of e(V)). clear sysuse auto keep for turn logistic for turn, coef matrix V = e(V) predict xb,xb gen myxb = _b[_cons] + _b[turn]*turn list xb myxb in 1 predict stdp,stdp list xb stdp in 1 mat X = J(1,2,0) mat X[1,1]=turn[1] mat X[1,2]=1 mat list X matrix XVX = X*V*X' di sqrt(XVX[1,1]) Now this was just getting the standard error for the linear predictor for the first observation. I could repeat this for each observation if I wanted. But I can take advantage of Stata's neat matrix functions to compute a bunch of these guys at one time. I'll do just the first five, so you can see what I mean: clear sysuse auto keep for turn logistic for turn, coef matrix V = e(V) keep in 1/5 predict stdp,stdp list stdp gen cons = 1 mkmat turn cons , matrix(X) matrix XVX = X*V*X' di sqrt(XVX[1,1]) di sqrt(XVX[2,2]) di sqrt(XVX[3,3]) di sqrt(XVX[4,4]) di sqrt(XVX[5,5]) Now, the only thing that is not slick now is the last piece where I take the squareroot of each diagonal entry. Here is a neat trick for that: clear sysuse auto keep for turn logistic for turn, coef matrix V = e(V) keep in 1/20 predict stdp,stdp gen cons = 1 mkmat turn cons , matrix(X) matrix XVX = X*V*X' matrix v = vecdiag(XVX) matrix se = vecdiag(cholesky(diag(v)))' svmat se list stdp se1 If you try this with many more observations you will probably have to increase your matsize (see -help matsize-). -- May mmb@stata.com * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**st: predict stdp after logistic regression;***From:*"G. ter Riet" <G.terRiet@amc.uva.nl>

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