Blend {Blendstat}

Joint analysis of experiments with mixtures and random effects.

Description

Joint analysis of experiments with mixtures and random effects, taking on a process variable represented by a covariable.

Usage

Blend(exp, X, Y, conc = NULL, effects = NULL)

Arguments

exp

Vector with the names of the experiments.

X

Mixture variables (components), without the vector of the concentrations (covariable).

Y

Response variable.

conc

Vector with the concentrations (covariable) of the experiments.

effects

Vector of the effects of the mixtures in a reference mixture (example: centroid).

Value

MPred

Matrix with the predicted and observed values.

MCPred

Matrix with the values predicted by components.

Mexp

Matrix with the design of the experiments.

theta

Vector with the theta estimates.

Author(s)

Marcelo Angelo Cirillo

Paulo Cesar Ossani

References

Kalirajan, K. P. On the estimation of a regression model with fixed and random coefficients. Journal of Applied Statistics, 17(2): 237-244, 1990. doi:10.1080/757582835

Swany, P. A. V. B. Statistical Inference in Random Coefficient Regression Models. Amsterdam: Springer Science & Business Media, 1971. 209 p.

See Also

Plot.Blend

Examples

data(DataNAT) # dataset 

Exp <- DataNAT[,2]   # identification of experiments

X <- DataNAT[,3:6] # independent variable
Y <- DataNAT[,11]  # dependent variable 
 
# effects of the blends in a reference mixture 
Effects <- rep(c(-0.1,0,0.1,0.2,0.3,0.4,0.5,0.6,0.7),4) 

Conc <- as.matrix(DataNAT[,7]) # covariate (process variable)

Res <- Blend(exp = Exp, X = X, Y = Y, conc = Conc, effects = Effects)

print("Predicted and observed values"); Res$MPred
print("Values predicted by components:"); Res$MCPred
print("Design of the experiments:"); Res$Mexp
print("Estimates of the linear model parameters:"); Res$theta 

Tit <- c("Covariate (process variable)","Variable")

Xlab = "effects"  # label of the X axis
Ylab = "Predicted values"  # label of the Y axis

Plot.Blend(Res, titles = Tit, posleg = 2, xlabel = Xlab,
           ylabel = Ylab, boxleg = TRUE, color = TRUE,
           expcolor = c("goldenrod3","gray53","red2", "blue2"), 
           casc = TRUE)