R-Square in WLS
On Nov 18, 2012, at 21:32 , Thomas Lumley wrote:
On Fri, Nov 16, 2012 at 4:48 PM, frespider <frespider at hotmail.com> wrote:
Hi, I am fitting a weighted least square regression and trying to compute SSE,SST and SSReg but I am not getting SST = SSReg + SSE and I dont know what I am coding wrong. Can you help please?
For a start, you need to replace your mu and muZ by weighted means.
The -1 in the model formulas also suggests that there will be problems even in the non-weighted case. The addition formula for SSDs works for successive model reductions, so it is required that the span of the design matrix X contains the vector of all ones.
-thomas [snip]
############################## Y = Log(Z) Scale #################################### Yhat <- X%*%bhat # predicted values mu <- mean(Y) To <- Y - mu Er <- Y - Yhat Re <- Yhat - mu lgSST <- sum(Weights*(To)^2) # log SST lgSSE <- sum(Weights*(Er)^2) # log SSE lgSSR <- sum(Weights*(Re)^2) # log SSR lgR-sq <- lgSSR/lgSST ############################### Z Scale ###################################### Z <- exp(Y) muZ <- mean(Z) Zhat <- exp(Yhat+0.5*Sigma2) ToZ <- Z-muZ ErZ <- Z - Zhat ReZ <- Zhat - muZ SST <- sum(Weights*(ToZ)^2) # SST SSE <- sum(Weights*(ErZ)^2) # SSE SSR <- sum(Weights*(ReZ)^2) # SSR Rsq <- SSR/SST I don't understand what is wrong with the code. The sum square regression plus the sum square error do not add up to the sum square total in both the Y scale and Z scale. Y is a normal distribution and Z is log normally distributed. Where is the error? Also, is there a way to calculate the weighted sum square?
-thomas -- Thomas Lumley Professor of Biostatistics University of Auckland [[alternative HTML version deleted]]
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