Blend {Blendstat} R Documentation

## 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.

`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)

```

[Package Blendstat version 1.0.3 Index]