| calc_ss {lazy.sasef} | R Documentation |
Calculation of SS associated with SAS Estimable Functions
calc_ss(obj = NULL, y = NULL, print = 0)
obj |
A design object |
y |
The response variable vector |
print |
= 1 to print the result |
A design object is a list of the design matrix (X),
infomation list (info) and parameter list (param) where
X is the design matrix
info is a list whose length is the number of effects:
info[[i]] contains the following:
ename name of effect[i]
order order of effect[i]: 0, 1, ..., maxorder
elevels # of levels of effect[i]
df degrees of freedom of effect[i]
erange range of effect[i] in the estimable function
range=cbind(from,to) where
from is the starting independent colmn of effect[i] in X
to is the ending independent column of effect[i] in X
rangef=cbind(from,to) where
from is the starting colmn of effect[i] in X
to is the ending column of effect[i] in X
menum vector of main effect number involved in effect[i]
contained vector of effect numbers which contains effect[i]
where effect number is defined according to the order of column of X.
contains vector of effects which effect[i] contais.
param is a list consisting of
type, drop, maxorder, sort, pattern
ef Information of estimable function.
The SS associated with each of estimable function of effect i,
Qf[erange[i,1]:erange[i,2],,drop=0],
where Qf is the non-zero rows of Q matrix: Q[locnz,,drop=0],
can be calculated as:
ssq(y-X%*%betahat0) - ssq(y-X%*%betahat)
where betahat is the LS estimate of beta w/o constraints and
betahat0 is the LS estimate of beta with constraints
Qf[erange[i,1]:erange[i,2],,drop=0] %*% beta = 0
which is given as
betahat0=betahat-invtXX%*%t(Qfi)%*
%solve(Qfi%*%invtXX%*%t(Qfi))%*%(Qfi%*%betahat)
A matrix with SS and df
# 2 x 3 unbalanced factorial data # design matrix and the estimable functions d1 <- design_mat( du23[,1:2], type=-1, pattern="a" ) ef1 <- sasef( d1, type="I", print=1 ) ef2 <- sasef( d1, type="II", print=1 ) ef3 <- sasef( d1, type="III", print=1 ) # response variable y <- du23[,3] # calculate Ss SS1 <- calc_ss( ef1, y, print=1 ) SS2 <- calc_ss( ef2, y, print=1 ) SS3 <- calc_ss( ef3, y, print=1 ) # Comparison with # SS by native and existing functions. # Use zeo-sum design matrix in lm. options(contrasts=c(factor="contr.sum",ordered="contr.poly")) LM2 <- lm(y ~ A + B + A *B , data=du23) # type I SS anova(LM2) # library(car) # type II SS # Anova(LM2) # type III Ss # Anova(LM2,type="III") # 2 x 3 x 2 unbalanced factorial data # design matrix and the estimable functions d2 <- design_mat( du232[,1:3], type=-1, pattern="a", sort=1 ) ef21 <- sasef( d2, type="I", print=1 ) ef22 <- sasef( d2, type="II", print=1 ) ef23 <- sasef( d2, type="III", print=1 ) # response variable y <- du232[,4] # calculate Ss SS21 <- calc_ss( ef21, y, print=1 ) SS22 <- calc_ss( ef22, y, print=1 ) SS23 <- calc_ss( ef23, y, print=1 ) # Comparison with # SS by native and existing functions. # Use zeo-sum design matrix in lm. options(contrasts=c(factor="contr.sum",ordered="contr.poly")) LM2 <- lm(y ~ A*B*C , data=du232) # type I SS anova(LM2) # library(car) # type II SS # Anova(LM2) # type III Ss # Anova(LM2,type="III")