Feed: Feed Intake and Weight Gain

In byandell/pda: Practial Data Analysis for Designed Experiments

Description

A scientist in food microbiology and toxicology (Chin et al. 1994) examined the effect of additives on weight gain in animals. He considered two levels (0.25% and 0.5%) of an additive CLA, a control and another additive (0.5% LA), which were labelled, respectively, as 1, 2, 3, 4. The initial concern was the tremendous differences in spread of weight gain for the four treatments. Plots of weight gain against feed intake (Figure XX) showed that this could be readily explained by feed intake. The feed intake slope is significant (p = 0.0088), as is the difference between LA and CLA (p = 0.0082) and the linear effect of %CLA (p = 0.013). The p-values are all computed using a Type III approach. Further, the effect of additive level seems to be linear and uncorrelated with the feed intake.

Usage

data(Feed)

Format

Feed data frame with 12 observations on 7 variables.

[,1]	trt	factor	treatment identifier
[,2]	bwt	numeric	body weight
[,3]	bwg	numeric	body weight gain
[,4]	fi	numeric	feed intake
[,5]	fe	numeric	feed(?)
[,6]	cla	numeric	CLA amount
[,6]	la	numeric	LA amount

Source

SF Chin

References

Chin SF, Storkson JM, Albright KJ, Cook ME and Pariza MW (1994) 'Conjugated linoleic acid is a growth factor for rats as shown by enhanced weight gain and imporved feed efficiency', J. Nutrition 124, 2344-2349.

Examples

data( Feed )
Feed$trt <- factor( Feed$trt )
levels( Feed$trt ) = c("25CLA","5CLA","CTRT","LA5")

# adjusted treatment -- analysis of covariance
Feed.ancova <- aov( bwg ~ trt + fi, Feed )
# regression type fit
Feed.reg <- aov( bwg ~ fi + la + cla, Feed )
# simple regression
Feed.fi <- aov( bwg ~ fi, Feed)

# removing factor or covariate
Feed$bwgfi <- resid( Feed.fi ) + lsmean( Feed.fi )$pred
Feed.fi2 <- aov( bwgfi ~ fi + trt, Feed )
Feed.fi1 <- aov( bwgfi ~ trt, Feed )
Feed.trt <- aov( bwg ~ trt, Feed )
Feed$bwgtrt <- resid( Feed.trt ) + lsmean( Feed.trt, fac = NULL )$pred
Feed.trt2 <- aov( bwgtrt ~ fi + trt, Feed )
Feed.trt1 <- aov( bwgtrt ~ fi, Feed )

# checking for any interaction
Feed.int <- aov( bwg ~ fi * trt, Feed )
Feed$res <- resid( Feed.ancova )
Feed.res <- aov( res ~ fi * trt, Feed )
# checking for high interaction
Feed$hi <- as.numeric((Feed$cla + Feed$la) == .5)
Feed.hi <- aov( bwg ~ fi + trt + fi:hi, Feed )

# Figure F:17.1 Feed treatment adjusted for intake
## regression lines in following plot are not parallel
## want reg lines from Feed.reg
print( xyplot( bwg ~ fi, Feed, groups = trt,
  type = "p", pch = levels( Feed$trt ), cex = 2,
  col = 1 + seq( length( levels( Feed$trt ))),
  panel = function(x,y,...) {
    panel.superpose(x,y,...)
    pred = predict( Feed.reg )
    pch = levels( Feed$trt )
    col = 1 + seq( along = pch )
    lty = c(3,4,1,2)
    for( i in col - 1 ) {
      ii = Feed$trt == pch[i]
      panel.lines( x[ii], pred[ii], col = col[i], lty = lty[i] )
    }
    tmp = mean( x )
    panel.abline( v = tmp, lty = 4 )
    # least squares means at same
    panel.points( rep( tmp, 4 ), predict( Feed.reg,
      data.frame( la = Feed$la[!duplicated(Feed$trt)],
                 cla = Feed$cla[!duplicated(Feed$trt)],
                 fi = rep( tmp, 4 ) ) ), pch = 18 )
    panel.points( tapply( x, Feed$trt, mean ),
      tapply( y, Feed$trt, mean ), pch = 0 )
  },
  xlab = "Feed intake", ylab = "weight gain",
  main = "Figure F:17.1 Feed treatment adjusted for intake" ))
data.frame(se.bar( 2700, 1350, std.dev( Feed.ancova ), cap = "SD" ))

# Figure F:17.3 Feed ancove residuals with plot symbols
tmpdata = data.frame( x = fitted( Feed.ancova ),
  y = resid( Feed.ancova ), trt = Feed$trt )
print( xyplot( y ~ x, tmpdata, groups = trt, type = "p",
  panel = function(x,y,...) {
    panel.superpose(x,y,...)
    panel.abline( h = 0, lty = 2 )
    panel.abline( h = c(-1,1) * std.dev( Feed.ancova ), lty = 3 )
  },
  xlab = "fitted", ylab = "residual",
  main = "Figure F:17.1 Feed treatment adjusted for intake" ))

tmpfn = function(x,y,lty=c(3,4,1,2), col = 2:5 ) {
  pch = levels( Feed$trt )
  for( i in seq( along = pch )) {
    ii = pch[i] == Feed$trt
    panel.lines( x[ii], y[ii], lty = lty[i], col = col[i] )
  }
}
# Figure F:17.4 Feed residuals and confounding
print( xyplot( bwgfi ~ fi, Feed, group = trt, type = "p",
  col = 2:5, pch = levels( Feed$trt ), cex = 2,
  panel = function(x,y,...) {
    panel.superpose(x,y,...)
    tmpfn( x, fitted( Feed.fi1 ), rep(1,4) )
    tmpfn( x, fitted( Feed.fi2 ), rep(2,4) )
    tmp <- mean( x )
    ## vertical line at fi mean
    panel.abline( h = lsmean(Feed.fi)$pred, lty = 3 )
    panel.abline( v = tmp, lty = 3 )
    ## least squares means at same
    panel.points( rep( tmp, 4 ), predict( Feed.fi2,
        data.frame( trt = unique( Feed$trt ), fi = rep( tmp, 4 ))),
      pch = 18 )
    panel.points( tapply( x, Feed$trt, mean ),
      tapply( y, Feed$trt, mean ), pch = 0 )
  },
  xlab = "(a) weight gain adjusted for Feed intake",
  ylab = "residual weight gain",
  main = "Figure F:17.4" ),
  more = TRUE, split = c(1,1,2,1) )
data.frame(se.bar( 2700, 1475, std.dev( Feed.fi2 ), cap = "SD" ))

print( xyplot( bwgtrt ~ fi, Feed, group = trt, type = "p",
  col = 2:5, pch = levels( Feed$trt ), cex = 2,
  panel = function(x,y,...) {
    panel.superpose(x,y,...)
    tmpfn( x, fitted( Feed.trt1 ), rep(1,4), rep(1,4) )
    tmpfn( x, fitted( Feed.trt2 ), rep(2,4) )
    tmp <- mean( x )
    panel.abline( h = lsmean(Feed.trt)$pred, lty = 3 )
    panel.abline( v = tmp, lty = 3 )
    panel.points( rep( tmp, 4 ), predict( Feed.trt2,
        data.frame( trt = unique( Feed$trt ), fi = rep( tmp, 4 ))),
      pch = 18 )
    panel.points( tapply( x, Feed$trt, mean ),
      tapply( y, Feed$trt, mean ), pch = 0 )
  },
  xlab = "(b) weight gain adjusted for treatment",
  ylab = "residual weight gain",
  main = "Feed residuals and confounding" ),
  split = c(2,1,2,1) )
data.frame(se.bar( 2700, 1350, std.dev( Feed.trt2 ), cap = "SD" ))

# Figure F:17.5 Feed evidence for different slopes
print( xyplot( bwg ~ fi, Feed, group = trt, type = "p",
  col = 2:5, pch = levels( Feed$trt ), cex = 2,
  panel = function(x,y,...) {
    panel.superpose(x,y,...)
    tmp <- mean( x )
    panel.abline( v = tmp, lty = 3 )
    panel.points( rep( tmp, 4 ), predict( Feed.int,
        data.frame( trt = unique( Feed$trt ), fi = rep( tmp, 4 ))),
      pch = 18 )
    panel.points( tapply( x, Feed$trt, mean ),
      tapply( y, Feed$trt, mean ), pch = 0 )
    tmpfn( x, fitted( Feed.int ))
  },
   xlab = "(a) different slopes", ylab = "weight gain",
  main = "Figure F:17.5" ),
  more = TRUE, split = c(1,1,2,1) )
data.frame(se.bar( 2700, 1325, std.dev( Feed.int ), cap = "SD int" ))
data.frame(se.bar( 2690, 1325, std.dev( Feed.ancova ), cap = "add SD", adj = 1 ))

Feed$pred = fitted( Feed.ancova )
print( xyplot( res ~ pred, Feed, group = trt, type = "p",
  col = 2:5, pch = levels( Feed$trt ), cex = 2,
  panel = function(x,y,...) {
    panel.superpose(x,y,...)
    tmp <- mean( x )
    panel.abline( h = 0, lty = 5 )
    panel.points( tapply( x, Feed$trt, mean ),
      tapply( y, Feed$trt, mean ), pch = 0 )
    tmpfn( x, fitted( Feed.res ))
  },
  xlab = "(b) pure interaction", ylab = "additive residual",
  main = "Feed evidence for different slopes" ),
  split = c(2,1,2,1) )

byandell/pda documentation built on May 13, 2019, 9:27 a.m.