nWayAOV | R Documentation |

Computes a single Bayes factor, or samples from the posterior, for an ANOVA model defined by a design matrix

nWayAOV( y, X, gMap, rscale, iterations = 10000, progress = getOption("BFprogress", interactive()), callback = function(...) as.integer(0), gibbs = NULL, posterior = FALSE, ignoreCols = NULL, thin = 1, method = "auto", continuous = FALSE, noSample = FALSE )

`y` |
vector of observations |

`X` |
design matrix whose number of rows match |

`gMap` |
vector grouping the columns of |

`rscale` |
a vector of prior scale(s) of appropriate length (see Details). |

`iterations` |
Number of Monte Carlo samples used to estimate Bayes factor or posterior |

`progress` |
if |

`callback` |
callback function for third-party interfaces |

`gibbs` |
will be deprecated. See |

`posterior` |
if |

`ignoreCols` |
if |

`thin` |
MCMC chain to every |

`method` |
the integration method (only valid if |

`continuous` |
either FALSE if no continuous covariates are included, or a logical vector of length equal to number of columns of X indicating which columns of the design matrix represent continuous covariates |

`noSample` |
if |

This function is not meant to be called by end-users, although
technically-minded users can call this function for flexibility beyond what
the other functions in this package provide. See `lmBF`

for a
user-friendly front-end to this function. Details about the priors can be
found in the help for `anovaBF`

and the references therein.

Argument `gMap`

provides a way of grouping columns of
the design matrix as a factor; the effects in each group will share a common
*g* parameter. `gMap`

should be a vector of the same length as the number of
nonconstant rows in `X`

. It will contain all integers from 0 to
*Ng-1*, where *Ng* is the total number of *g*
parameters. Each element of `gMap`

specifies the group to which that
column belongs.

If all columns belonging to a group are adjacent, `struc`

can instead
be used to compactly represent the groupings. `struc`

is a vector of
length *Ng*. Each element specifies the number columns in the
group.

The vector `rscale`

should be of length *Ng*, and contain the
prior scales of the standardized effects. See Rouder et al. (2012) for more
details and the help for `anovaBF`

for some typical values.

The method used to estimate the Bayes factor depends on the `method`

argument. "simple" is most accurate for small to moderate sample sizes, and
uses the Monte Carlo sampling method described in Rouder et al. (2012).
"importance" uses an importance sampling algorithm with an importance
distribution that is multivariate normal on log(g). "laplace" does not
sample, but uses a Laplace approximation to the integral. It is expected to
be more accurate for large sample sizes, where MC sampling is slow. If
`method="auto"`

, then an initial run with both samplers is done, and
the sampling method that yields the least-variable samples is chosen. The
number of initial test iterations is determined by
`options(BFpretestIterations)`

.

If posterior samples are requested, the posterior is sampled with a Gibbs sampler.

If `posterior`

is `FALSE`

, a vector of length 2 containing
the computed log(e) Bayes factor (against the intercept-only null), along
with a proportional error estimate on the Bayes factor. Otherwise, an
object of class `mcmc`

, containing MCMC samples from the posterior is
returned.

Argument `struc`

has been deprecated. Use `gMap`

, which is the `inverse.rle`

of `struc`

,
minus 1.

Richard D. Morey (richarddmorey@gmail.com), Jeffery N. Rouder (rouderj@missouri.edu)

Rouder, J. N., Morey, R. D., Speckman, P. L., Province, J. M., (2012) Default Bayes Factors for ANOVA Designs. Journal of Mathematical Psychology. 56. p. 356-374.

See `lmBF`

for the user-friendly front end to this
function; see `regressionBF`

and `anovaBF`

for testing
many regression or ANOVA models simultaneously.

## Classical example, taken from t.test() example ## Student's sleep data data(sleep) plot(extra ~ group, data = sleep) ## traditional ANOVA gives a p value of 0.00283 summary(aov(extra ~ group + Error(ID/group), data = sleep)) ## Build design matrix group.column <- rep(1/c(-sqrt(2),sqrt(2)),each=10) subject.matrix <- model.matrix(~sleep$ID - 1,data=sleep$ID) ## Note that we include no constant column X <- cbind(group.column, subject.matrix) ## (log) Bayes factor of full model against grand-mean only model bf.full <- nWayAOV(y = sleep$extra, X = X, gMap = c(0,rep(1,10)), rscale=c(.5,1)) exp(bf.full[['bf']]) ## Compare with lmBF result (should be about the same, give or take 1%) bf.full2 <- lmBF(extra ~ group + ID, data = sleep, whichRandom = "ID") bf.full2

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