R Under development (unstable) (2023-08-12 r84939 ucrt) -- "Unsuffered Consequences"
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> library(survival)
> aeq <- function(x, y, ...) all.equal(as.vector(x), as.vector(y), ...)
> 
> fit1 <- lm(skips ~ Opening + Solder + Mask + PadType + Panel,
+               data=solder)
> y1 <- yates(fit1, "Opening")
> 
> temp <- levels(solder$Opening)
> tpred <- matrix(0., nrow(solder), 3)
> for (i in 1:3) {
+     tdata <- solder
+     tdata$Opening <- temp[i]
+     tpred[,i] <- predict(fit1, newdata=tdata)
+  }
> all.equal(y1$estimate[,"pmm"], colMeans(tpred))
[1] TRUE
> 
> # This fit is deficient: there are no Opening=L and Mask=A6 obs
> # The MPV for Mask=A6 and Opening L will therefore be NA, as well
> #   as for all levels of Solder, but we can compute the others.
> # Solder will be NA for all levels
> fit2 <- lm(skips ~ Opening*Mask + Solder,
+               data=solder)
> y2a <- yates(fit2, "Mask", population="factorial")
> y2b <- yates(fit2, "Opening",  population="factorial")
> y2c <- yates(fit2, "Solder",  population="factorial")
> 
> # The predict.lm function gives correct predictions for estimable
> #  functions (all but L,A6) and nonsense for others.  It knows that
> #  some are not estimable due to the NA coefficients, but not which ones,
> #  so always prints a warning.  Hence the suppressWarnings call.
> tdata <- do.call(expand.grid, fit2$xlevels[1:3])
> temp <- levels(solder$Mask)
> tpreda <- matrix(0., nrow(tdata), length(temp),
+                  dimnames=list(NULL, temp))
> for (i in seq(along=temp)) {
+     tdata$Mask <- temp[i]
+     suppressWarnings(tpreda[,i] <- predict(fit2, newdata=tdata))
+  }
> tpreda[,"A6"] <- NA  # the A6 estimate is deficient
> aeq(y2a$estimate[,"pmm"], colMeans(tpreda))
[1] TRUE
> 
> tdata <- do.call(expand.grid, fit2$xlevels[1:3])
> temp <- levels(solder$Opening)
> tpredb <- matrix(0., nrow(tdata), length(temp),
+                  dimnames=list(NULL, temp))
> for (i in seq(along=temp)) {
+     tdata$Opening <- temp[i]
+     suppressWarnings(tpredb[,i] <- predict(fit2, newdata=tdata))
+  }
> tpredb[,"L"] <- NA  
> aeq(y2b$estimate[,"pmm"], colMeans(tpredb))
[1] TRUE
> 
> # Solder should be all NA
> all(is.na(y2c$estimate[,"pmm"]))
[1] TRUE
> 
> # Tests for Solder are defined for a non-factorial population, however.
> # the [] below retains the factor structure of the variable, where the
> #  runs above did not.  R gets prediction correct  both ways.
> y2d <- yates(fit2, ~Solder)
> temp <- levels(solder$Solder)
> tdata <- solder
> tpredd <- matrix(0, nrow(tdata), length(temp),
+                  dimnames=list(NULL, temp))
> for (i in seq(along=temp)) {
+     tdata$Solder[] <- temp[i]
+     suppressWarnings(tpredd[,i] <- predict(fit2, newdata=tdata))
+ }
> aeq(y2d$estimate$pmm, colMeans(tpredd))
[1] TRUE
> 
> #
> # Verify that the result is unchanged by how dummies are coded
> #   The coefs move all over the map, but predictions are unchanged
> fit3 <- lm(skips ~ C(Opening, contr.helmert)*Mask + C(Solder, contr.SAS),
+            data=solder)
> y3a <- yates(fit3, ~Mask, population='yates')
> equal <- c("estimate", "test", "mvar")
> all.equal(y3a[equal], y2a[equal])
[1] TRUE
> 
> tdata <- do.call(expand.grid, fit2$xlevels[1:3]) # use orignal variable names
> temp <- levels(solder$Mask)
> cpred <- matrix(0., nrow(tdata), length(temp),
+                  dimnames=list(NULL, temp))
> for (i in seq(along=temp)) {
+     tdata$Mask <- temp[i]
+     suppressWarnings(cpred[,i] <- predict(fit3, newdata=tdata))
+  }
> aeq(cpred[, temp!="A6"], tpreda[, temp!= "A6"])  # same predictions
[1] TRUE
> all.equal(y3a$estimate, y2a$estimate)
[1] TRUE
> 
> y3b <- yates(fit3, ~Opening, population='yates')
> # column names will differ
> all.equal(y3b$estimate, y2b$estimate, check.attributes=FALSE)
[1] TRUE
> 
> y3d <- yates(fit3, ~Solder)
> for (i in 1:3) {
+     print(all.equal(y3d[[i]], y2d[[i]], check.attributes=FALSE))
+ }
[1] TRUE
[1] TRUE
[1] TRUE
> 
> # Reprise this with a character variable in the model
> sdata <- solder
> sdata$Mask <- as.character(sdata$Mask)
> fit4 <-  lm(skips ~ Opening*Mask + Solder, data=sdata)
> y4a <- yates(fit4, ~ Mask, population= "yates")
> y4b <- yates(fit4, ~ Opening, population= "yates")
> y4d <- yates(fit4, ~ Solder)
> equal <- c("estimate", "tests", "mvar", "cmat")
> all.equal(y2a[equal], y4a[equal])  # the "call" component differs
[1] TRUE
> all.equal(y2b[equal], y4b[equal])
[1] TRUE
> all.equal(y2d[equal], y4d[equal])
[1] TRUE
> 
> proc.time()
   user  system elapsed 
   1.43    0.17    1.59