Assay data frame has 60 rows and 4 columns.
This data frame contains the following columns:
an factor with levels
identifying the block of the well
a factor with levels
f identifying the
sample corresponding to the well
an ordered factor with levels
indicating the dilution applied to the well
a numeric vector of the log-optical density
These data, courtesy of Rich Wolfe and David Lansky from Searle, Inc., come from a bioassay run on a 96-well cell culture plate. The assay is performed using a split-block design. The 8 rows on the plate are labeled A–H from top to bottom and the 12 columns on the plate are labeled 1–12 from left to right. Only the central 60 wells of the plate are used for the bioassay (the intersection of rows B–G and columns 2–11). There are two blocks in the design: Block A contains columns 2–6 and Block B contains columns 7–11. Within each block, six samples are assigned randomly to rows and five (serial) dilutions are assigned randomly to columns. The response variable is the logarithm of the optical density. The cells are treated with a compound that they metabolize to produce the stain. Only live cells can make the stain, so the optical density is a measure of the number of cells that are alive and healthy.
Pinheiro, J. C. and Bates, D. M. (2000), Mixed-Effects Models in S and S-PLUS, Springer, New York. (Appendix A.2)
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str(Assay) m1 <- lmer(logDens ~ sample * dilut + (1|Block) + (1|Block:sample) + (1|Block:dilut), Assay, verbose = TRUE) print(m1, corr = FALSE) anova(m1) m2 <- lmer(logDens ~ sample + dilut + (1|Block) + (1|Block:sample) + (1|Block:dilut), Assay, verbose = TRUE) print(m2, corr = FALSE) anova(m2) m3 <- lmer(logDens ~ sample + dilut + (1|Block) + (1|Block:sample), Assay, verbose = TRUE) print(m3, corr = FALSE) anova(m3) anova(m2, m3)
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