Description Usage Arguments Value Author(s) References Examples

`mixed.mdmr`

allows users to conduct multivariate distance matrix
regression (MDMR) in the context of a (hierarchically) clustered sample
without inflating Type-I error rates as a result of the violation of the
independence assumption. This is done by invoking a mixed-effects modeling
framework, in which clustering/grouping variables are specified as random
effects and the covariate effects of interest are fixed effects. The input
to `mixed.mdmr`

largely reflects the input of the `lmer`

function from the package `lme4`

insofar as the specification of
random and fixed effects are concerned (see Arguments for details). Note that
this function simply controls for the random effects in order to test the
fixed effects; it does not facilitate point estimation or inference on the
random effects.

1 2 | ```
mixed.mdmr(fmla, data, D = NULL, G = NULL, use.ssd = 1,
start.acc = 1e-20, ncores = 1)
``` |

`fmla` |
A one-sided linear formula object describing both the fixed-effects and random-effects part of the model, beginning with an ~ operator, which is followed by the terms to include in the model, separated by + operators. Random-effects terms are distinguished by vertical bars (|) separating expressions for design matrices from grouping factors. Two vertical bars (||) can be used to specify multiple uncorrelated random effects for the same grouping variable. |

`data` |
A mandatory data frame containing the variables named in formula. |

`D` |
Distance matrix computed on the outcome data. Can be either a
matrix or an R |

`G` |
Gower's centered similarity matrix computed from |

`use.ssd` |
The proportion of the total sum of squared distances (SSD)
that will be targeted in the modeling process. In the case of non-Euclidean
distances, specifying |

`start.acc` |
Starting accuracy of the Davies (1980) algorithm
implemented in the |

`ncores` |
Integer; if |

An object with six elements and a summary function. Calling
`summary(mixed.mdmr.res)`

produces a data frame comprised of:

`Statistic` |
Value of the corresponding MDMR test statistic |

`Numer DF` |
Numerator degrees of freedom for the corresponding effect |

`p-value` |
The p-value for each effect. |

In addition to the information in the three columns comprising
`summary(res)`

, the `res`

object also contains:

`p.prec` |
A data.frame reporting the precision of each p-value. If
analytic p-values were computed, these are the maximum error bound of the
p-values reported by the |

Note that the printed output of `summary(res)`

will truncate p-values
to the smallest trustworthy values, but the object returned by
`summary(res)`

will contain the p-values as computed. The reason for
this truncation differs for analytic and permutation p-values. For an
analytic p-value, if the error bound of the Davies algorithm is larger than
the p-value, the only conclusion that can be drawn with certainty is that
the p-value is smaller than (or equal to) the error bound.

Daniel B. McArtor (dmcartor@gmail.com) [aut, cre]

Davies, R. B. (1980). The Distribution of a Linear Combination of chi-square Random Variables. Journal of the Royal Statistical Society. Series C (Applied Statistics), 29(3), 323-333.

Duchesne, P., & De Micheaux, P. L. (2010). Computing the distribution of quadratic forms: Further comparisons between the Liu-Tang-Zhang approximation and exact methods. Computational Statistics and Data Analysis, 54(4), 858-862.

McArtor, D. B. (2017). Extending a distance-based approach to multivariate multiple regression (Doctoral Dissertation).

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 | ```
data("clustmdmrdata")
# Get distance matrix
D <- dist(Y.clust)
# Regular MDMR without the grouping variable
mdmr.res <- mdmr(X = X.clust[,1:2], D = D, perm.p = FALSE)
# Results look significant
summary(mdmr.res)
# Account for grouping variable
mixed.res <- mixed.mdmr(~ x1 + x2 + (x1 + x2 | grp),
data = X.clust, D = D)
# Signifance was due to the grouping variable
summary(mixed.res)
``` |

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