fractional_factorial_efficiency {ExpertChoice} | R Documentation |

Fractional Factorial Design Efficiency

```
fractional_factorial_efficiency(formula, searched_fractional_factorial)
```

`formula` |
A specification, in formula form, of the desired effects sought to be estimated. |

`searched_fractional_factorial` |
a fractional factorial generated as the result of a 'search_design'. |

a list with the following objects: 1. X - This is the formula expanded version of the fractional factorial which was passed to the function. 2. information_mat - This is the information matrix described by the associated note. Note: it is rounded to three decimal places to ease reading. 3. inv_information_mat - This is the inverse of the information matrix. Note: it is rounded to three decimal places to ease reading. 4. lamda_mat - This is the diagonal elements of the Lamda Matrix described by Kuhfeld (pg. 62). The elements are the eigen values of the inv_information_mat. 5. inv_diag - This is the diagonal elements of the inv_information_mat. (May be of use to some researchers...) 6. GWLP - This is the generalised world lengths for the searched design. (Note: this would not change depending on what is in the formula expansion.) 7. A_eff - This is the A-efficiency of the design given the particular formula expansion. 8. D_eff - This is the D-efficiency of the design given the particular formula expansion.

Kuhfeld, W. F. Marketing Research Methods in SAS Experimental Design, Choice, Conjoint, and Graphical Techniques 2010.

```
# See step 5 of the Practical Introduction to ExpertChoice vignette.
# Step 1
attrshort = list(condition = c("0", "1", "2"),
technical =c("0", "1", "2"),
provenance = c("0", "1"))
#Step 2
# ff stands for "full fatorial"
ff <- full_factorial(attrshort)
af <- augment_levels(ff)
# af stands for "augmented factorial"
# Step 3
# Choose a design type: Federov or Orthogonal. Here an Orthogonal one is used.
nlevels <- unlist(purrr::map(ff, function(x){length(levels(x))}))
fractional_factorial <- DoE.base::oa.design(nlevels = nlevels, columns = "min34")
# Step 4
# The functional draws out the rows from the original augmented full factorial design.
colnames(fractional_factorial) <- colnames(ff)
fractional <- search_design(ff, fractional_factorial)
# Step 5! - The fractional_factorial_efficiency function
# The formula requires reference to the original attributes of the design.
# Check for the main effects.
fractional_factorial_efficiency(~ condition + technical + provenance, fractional)
# Check for the main effects with some interaction.
fractional_factorial_efficiency(~ condition + technical * provenance, fractional)
```

[Package *ExpertChoice* version 0.2.0 Index]