Hi Peter,
why you are involving -1 with this concept? Can you explain more please
Cheers
Date: Sun, 18 Nov 2012 23:28:26 -0800
From: ml-node+s789695n4650012...@n4.nabble.com
To: frespi...@hotmail.com
Subject: Re: R-Square in WLS
On Nov 18, 2012, at 21:32 , Thomas Lumley wrote:
> On Fri, Nov 16, 2012 at 4:48 PM, frespider <[hidden email]> 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
>
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>
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--
Peter Dalgaard, Professor,
Center for Statistics, Copenhagen Business School
Solbjerg Plads 3, 2000 Frederiksberg, Denmark
Phone: (+45)38153501
Email: [hidden email] Priv: [hidden email]
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