Dear list,

this seemed to me like a very trivial question, but finally I haven't found

any similar postings with suitable solutions on the net ...

Basically, instead of regressing two simple series of measures 'a' and 'b'

(like b ~ a), I would like to use independent replicate measurements for

each variable at each level (ie, instead of having just one 'a' and one 'b'

I have independent replicates for all measures of 'a' and 'b', 'a1' could

be as well compared to 'b1' as to 'b2' etc.)

In analogy one could think of a procedure claiming to act and increase a

given output value by eg 30% (compared to not emplying this procedure).

Now I have indepedent repeated measures (since the measures themselves are

considered not very precise) for a (large) number of individuals with and

without the treatment.

Basically, I want to test the hypthesis that applying the procedure

increases values in a linear way by a given factor, thus test the

parameters of a linear regression (eg slope=1.3, offset may be different to

0). In extension to this, how could I make a confidence-interval for the

estimated slop (due to the treatment) to check if the claimed value is

indeed inside ?

# Here some toy data, my real data are much larger and might ressemble

somehow to this.

# Lines are for subjects and columns for 2 groups and repeat-measurements.

# in this case I introduce a toy-factor of 1.3 to the 2nd part of my data

(in the real data such a factor is just a hypothesis), which I would like

to investigate/confirm

dat <- matrix(rep(1:12,7)+rnorm(84),nc=7)

dat[,4:7] <- 1.3*dat[,4:7]+runif(48)

# some individual measures may be missing :

dat[2:3,4] <- NA

colnames(dat) <- paste(rep(c("a","b"),3:4),c(1:3,1:4),sep="")

# In analogy to the ample documentation of lm() :

datMean <- cbind(aM=rowMeans(dat[,1:3]),bM=rowMeans(dat[,4:7]))

(lmMean <- lm(bM ~ aM,data=as.data.frame(datMean)))

# I suppose the estimated parameters (intercet & slope) may be correct but

sice the degrees of freedom are not made of means I am convinced they are

incorrect and thus any statistics using them will be so, too ...

df.residual(lmMean)

summary(lmMean)

# I also thought about a workaround reorganizing the data into a 'simple'

two-column setup using somthing like stack() and allowing b ~ a, but again,

I suppose the degrees of freedom won't be correct neither.

# 1) should I simply correct the degrees of freedom in my lm-object, would

this be the correct number of degrees of freedom

lmMean$df.residual <- nrow(dat)*5-2

# then I suppose I would need to change the standard errors, I'm shur what

is the best way to do so

# or 2) is there a package allowing to do these steps, thus returning

correct DF, Std Err and Pr(>|t) ?

Thanks in advance,

Wolfgang Raffelsberger

for completeness :

sessionInfo()

> sessionInfo()

R version 3.4.4 (2018-03-15)

Platform: x86_64-w64-mingw32/x64 (64-bit)

Running under: Windows 7 x64 (build 7601) Service Pack 1

Matrix products: default

locale:

[1] LC_COLLATE=French_France.1252 LC_CTYPE=French_France.1252

LC_MONETARY=French_France.1252

[4] LC_NUMERIC=C LC_TIME=French_France.1252

attached base packages:

[1] stats graphics grDevices utils datasets methods base

other attached packages:

[1] limma_3.34.9 lme4_1.1-15 Matrix_1.2-12 TinnRcom_1.0.20

formatR_1.4 svSocket_0.9-57

loaded via a namespace (and not attached):

[1] Rcpp_0.12.16 lattice_0.20-35 MASS_7.3-49 grid_3.4.4

nlme_3.1-131.1 minqa_1.2.4

[7] nloptr_1.0.4 svMisc_0.9-70 splines_3.4.4 tools_3.4.4

compiler_3.4.4 tcltk_3.4.4

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