Description Usage Arguments Details Value Note Examples

Calculates a Williams' type test statistic for a constrained linear mixed effects model.

Williams' type statistic (individual)

1 2 3 | ```
w.stat(theta, cov.theta, B, A, ...)
w.stat.ind(theta, cov.theta, B, A, ...)
``` |

`theta` |
estimated coefficients. |

`cov.theta` |
covariance matrix of the (unconstrained) coefficients. |

`B` |
matrix to obtain the global contrast. |

`A` |
matrix of linear constraints. |

`...` |
additional arguments, to enable custom test statistic functions. |

See `create.constraints`

for an example of `A`

. Argument `B`

is similar, but defines the global contrast for a Williams' type test statistic. This is the largest hypothesized difference in the constrained coefficients. So for an increasing simple order, the test statistic is the difference between the two extreme coefficients, *theta_1* and *theta_p1*, divided by the standard error (unconstrained). For an umbrella order order, two contrasts are considered, *theta_1* to *theta_s*, and *theta_p1* to *theta_s*, each divided by the appropriate unconstrained standard error. A general way to express this statistic is:

*W = max theta_{B[i,2]} - theta_{B[i,1]} / sqrt( VAR( theta_{B[i,2]} - theta_{B[i,1]} ) )*

where the numerator is the difference in the constrained estimates, and the standard error in the denominator is based on the covariance matrix of the unconstrained estimates.

The function `w.stat.ind`

does the same, but uses the `A`

matrix which defines all of the individual constraints, and returns a test statistic for each constraints instead of taking the maximum.

Output is a numeric value.

See `lrt.stat`

for information on creating custom test statistics.

1 2 3 4 5 6 7 8 9 |

jelsema/CLME documentation built on May 25, 2018, 4:43 a.m.

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