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I am trying to fully understand the ins and outs of the plm package in R. I have a dataset where I computed a fixed effects plm:

mydata <- read.spss("G:/data.sav",use.value.labels=TRUE, to.data.frame = TRUE)

attach(mydata) 
Y <- cbind(Y) 
X <- cbind(x1,x2,x3) 

pdata <- plm.data(mydata, index=c("id","YEAR")) 
fixed <- plm(Y ~ X, data=pdata, model= "within") 

I am trying to calculate both the training and test dataset predicted values. I found some material on CV here that kind of addresses what I am trying to do, but does not completely answer it. When I calculate by hand:

y = beta1*z + beta2*z + theta*id 

the predicted values from

fitted <- as.numeric(fixed$model[[1]] - fixed$residuals) 

are not the same as when I sum beta*x1 + beta*x2 + beta*x3 + fixef(fixed). Basically I am trying to figure out how to calculate by hand the in sample predicted values so I can run the calculations for the out of sample data.

Can anyone explain what I maybe doing wrong in doing the calculation by hand?

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You need to extract the fixed effects by fixef and match them to the individual index. Here is an example for the Grunfeld data:

data(Grunfeld, package = "plm")
fe <- plm(inv ~ value + capital, data=Grunfeld, model = "within")

temp <- merge(Grunfeld, data.frame(fixef_firm = names(fixef(fe)), fixef = as.numeric(fixef(fe))), all.x =T, by.x = c("firm"), by.y=c("fixef_firm"))
fitted_by_hand <- temp$fixef + fe$coefficients[1] * Grunfeld$value +  fe$coefficients[2] * Grunfeld$capital

fitted <- fe$model[ , 1] - fe$residuals

# just to remove attributs and specific classes 
fitted_by_hand <- as.numeric(fitted_by_hand)
fitted <- as.numeric(fitted)

all.equal(fitted, fitted_by_hand) # TRUE
cbind(fitted, fitted_by_hand) # see yourself
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