Description Usage Arguments Details Value Note Author(s) References See Also Examples

Fits logistic regression models to each level of `group`

to
model the probability of two samples being analogues conditional upon
the dissimilarity between the two samples.

1 2 3 4 5 6 7 8 9 10 11 |

`object` |
for |

`groups` |
factor (or object that can be coerced to one) containing
the group membership for each sample in |

`k` |
numeric; the |

`biasReduced` |
logical; should Firth's method for bias reduced
logistic regression be used to fit the models? If |

`p` |
probability at which to predict the dose needed. |

`...` |
arguments passed to other methods. These arguments are
passed on to |

Fits logistic regression models to each level of `group`

to
model the probability of two samples being analogues (i.e. in the same
group) conditional upon the dissimilarity between the two samples.

This function can be seen as a way of directly modelling the
probability that two sites are analogues, conditional upon
dissimilarity, that can also be done less directly using
`roc`

and `bayesF`

.

Often, the number of true analogues in the training set is small, both
in absolute terms and as a proportion of comparisons. Logistic
regression is known to suffer from a small-sample bias. Firth's method
of bias reduction is a general solution to this problem and is
implemented in `logitreg`

through the brglm package of
Ioannis Kosmidis.

`logitreg`

returns an object of class `"logitreg"`

; a list
whose components are objects returned by `glm`

. See
`glm`

for further details on the returned objects.

The components of this list take their names from `group`

.

For `summary.logitreg`

an object of class
`"summary.logitreg"`

, a data frame with summary statistics of the
model fits. The components of this data frame are:

`In, Out` |
The number of analogue and non-analogue dissimilarities analysed in each group, |

`Est.(Dij), Std.Err` |
Coefficient and its standard error for dissimilarity from the logit model, |

`Z-value, p-value` |
Wald statistic and associated p-value for each logit model. |

`Dij(p=?), Std.Err(Dij)` |
The dissimilarity at which the posterior
probability of two samples being analogues is equal to |

The function may generate warnings from function
`glm.fit`

. These should be investigated and not simply
ignored.

If the message is concerns fitted probabilities being numerically 0 or
1, then check the fitted values of each of the models. These may well
be numerically 0 or 1. Heed the warning in `glm`

and read
the reference cited therein which **may** indicate problems with
the fitted models, such as (quasi-)complete separation.

Gavin L. Simpson

Firth, D. (1993). Bias reduction of maximum likelihood
estimates. *Biometrika* **80**, 27-38.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 | ```
## load the example data
data(swapdiat, swappH, rlgh)
## merge training and test set on columns
dat <- join(swapdiat, rlgh, verbose = TRUE)
## extract the merged data sets and convert to proportions
swapdiat <- dat[[1]] / 100
rlgh <- dat[[2]] / 100
## fit an analogue matching (AM) model using the squared chord distance
## measure - need to keep the training set dissimilarities
swap.ana <- analog(swapdiat, rlgh, method = "SQchord",
keep.train = TRUE)
## fit the ROC curve to the SWAP diatom data using the AM results
## Generate a grouping for the SWAP lakes
METHOD <- if (getRversion() < "3.1.0") {"ward"} else {"ward.D"}
clust <- hclust(as.dist(swap.ana$train), method = METHOD)
grps <- cutree(clust, 6)
## fit the logit models to the analog object
swap.lrm <- logitreg(swap.ana, grps)
swap.lrm
## summary statistics
summary(swap.lrm)
## plot the fitted logit curves
plot(swap.lrm, conf.type = "polygon")
## extract fitted posterior probabilities for training samples
## for the individual groups
fit <- fitted(swap.lrm)
head(fit)
## compute posterior probabilities of analogue-ness for the rlgh
## samples. Here we take the dissimilarities between fossil and
## training samples from the `swap.ana` object rather than re-
## compute them
pred <- predict(swap.lrm, newdata = swap.ana$analogs)
head(pred)
## Bias reduction
## fit the logit models to the analog object
swap.brlrm <- logitreg(swap.ana, grps, biasReduced = TRUE)
summary(swap.brlrm)
``` |

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