Extract Residuals of a 'VCA' Object
Function extracts marginal or conditional residuals from a 'VCA' object, representing a linear mixed model.
## S3 method for class 'VCA'
residuals(
object,
type = c("conditional", "marginal"),
mode = c("raw", "student", "standard", "pearson"),
quiet = FALSE,
...
)object |
(VCA) object |
type |
(character) string specifying the type of residuals to be returned, valid options are "marginal" and "conditional" or abbreviations |
mode |
(character) string or abbreviation specifying the specific transformation applied to a certain type of residuals. There are "raw" (untransformed), "standardized", "studentized" and "pearson" (see details) residuals. |
quiet |
(logical) TRUE = will suppress any warning, which will be issued otherwise |
... |
additional parameters |
There are two types of residuals which can be extraced from a 'VCA' object.
Marginal residuals correspond to e_m = y - y_hat, where y_hat = Xb with X
being the design matrix of fixed effects and b being the column vector of fixed
effects parameter estimates. Conditional residuals are defined as e_c = y - Xb - Zg,
where Z corresponds to the designs matrix of random effects g.
Whenever 'obj' is a pure-error model, e.g. 'y~1' both options will return the same values
y - Xb and b corresponds to the intercept.
Each type of residuals can be standardized, studentized, or transformed to pearson-type residuals.
The former corresponds to a transformation of residuals to have mean 0 and variance equal to 1 ([r - mean(r)]/sd(r)]).
Studentized residuals emerge from dividing raw residuals by the square-root of diagonal elements of the corresponding
variance-covariance matrix. For conditional residuals, this is Var(c) = P = RQR, with Q = V"(I - H),
H = XT being the hat-matrix, and T = (X'V"X)"X'V". For marginal residuals, this matrix
is Var(m) = O = V - Q. Here, >'< denotes the matrix transpose operator,
and >"< the regular matrix inverse. Pearson-type residuals are computed in the same manner as studentized, only
the variance-covariance matrices differ. For marginal residuals this is equal to Var(y) = V, for conditional residuals
this is Var(c) = R (see getV for details).
Andre Schuetzenmeister andre.schuetzenmeister@roche.com
Hilden-Minton, J. A. (1995). Multilevel diagnostics for mixed and hierarchical linear models. Dissertation, University of California, Los Angeles.
Nobre, J. S. & Singer, J. M. (2007). Residual analysis for linear mixed models. Biometrical Journal, 49, 863-875.
Schuetzenmeister, A. and Piepho, H.P. (2012). Residual analysis of linear mixed models using a simulation approach. Computational Statistics and Data Analysis, 56, 1405-1416
## Not run: data(VCAdata1) datS1 <- VCAdata1[VCAdata1$sample==1,] fit1 <- anovaVCA(y~(lot+device)/(day)/(run), datS1) # default is conditional (raw) residuals resid(fit1) resid(fit1, "m") # get standardized version resid(fit1, mode="stand") # conditional residuals (default) resid(fit1, "marg", "stand") # marginal residuals # get studentized version, taking their # covariances into account resid(fit1, mode="stud") # conditional residuals (default) resid(fit1, "marg", "stud") # marginal residuals ## End(Not run)
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