Fx_simplex: Matrix of candidate regressors for a regression model on a...
In OptimalDesign: A Toolbox for Computing Efficient Designs of Experiments

Description Usage Arguments Value Note Author(s) See Also Examples

Creates the matrix of all candidate regressors for a mixture regression model on a regular simplex grid (up to 9 factors).

1	Fx_simplex(formula, n.levels.mix=NULL, echo=TRUE)

`formula`	the formula of the model. The rules for creating the formula are standard for R but: 1) the formula must not contain the dependent variable (it is one-sided); 2) the `d` factors (variables) must be labeled `x1,x2,x3,`...
`n.levels.mix`	the number of levels of each factor (each factor has the same number of levels). If `n.levels=NULL`, the program sets `n.levels <- 2*d + 1`.
`echo`	Print the call of the function?

The n times m matrix of all candidate regressors of a mixture regression model on a regular simplex grid.

Note that Fx is not the design matrix (which is also sometimes called the regression matrix, or the model matrix). The design matrix depends on Fx as well as on the exact experimental design w. For this package, an exact experimental design is formalized as the vector of non-negative integer values corresponding to the replication of trials (observations) in individual design points. Thus, if Fx is the matrix of all candidate regressors and w is the exact design then Fx[rep(1:nrow(Fx), w),] is the actual design matrix for the experiment.

Radoslav Harman, Lenka Filova

Fx_cube, Fx_glm, Fx_dose, Fx_survival, Fx_blocks

## Not run: 
# The Fx of the Scheffe quadratic mixture model
# with 3 mixture components, each with 21 levels.
Fx <- Fx_simplex(~x1 + x2 + x3 + I(x1*x2) + I(x1*x3) + I(x2*x3) - 1, 21)

# The approximate I-optimal design of size 20
# bound by 1 at each design point
w <- od_MISOCP(Fx, b3=20, bin=TRUE, crit="I", type="approximate")$w.best
od_plot(Fx, w, Fx[, 2:3])

# As above, with constraints on the proportions
r <- c(); for (i in 1:nrow(Fx)) if (max(Fx[i, 2:4]) > 0.7) r <- c(r, i)
w <- od_MISOCP(Fx[-r, ], b3=20, bin=TRUE, crit="I", type="approximate")$w.best
od_plot(Fx[-r, ], w, Fx[-r, 2:3])

# Note that one must be careful when choosing a model for a mixture experiment:
# Let us compute the matrix of regressors of the simple linear mixture model
# with 4 mixture components, each with levels {0, 0.5, 1}.

Fx <- Fx_simplex(~x1 + x2 + x3 + x4, 3)

# The model has only 5 parameters and as many as 10 design points,
# but there is no design that guarantees estimability of the parameters.
# This can be shown by evaluating:
det(infmat(Fx, rep(1, 10)))

## End(Not run)