# ftrend: Fit a floating trend to a factor in generalized linear model In Epi: Statistical Analysis in Epidemiology

## Description

Fits a "floating trend" model to the given factor in a glm in a generalized linear model by centering covariates.

## Usage

 `1` ```ftrend(object, ...) ```

## Arguments

 `object` fitted `lm` or `glm` object. The model must not have an intercept term `...` arguments to the `nlm` function

## Details

`ftrend()` calculates "floating trend" estimates for factors in generalized linear models. This is an alternative to treatment contrasts suggested by Greenland et al. (1999). If a regression model is fitted with no intercept term, then contrasts are not used for the first factor in the model. Instead, there is one parameter for each level of this factor. However, the interpretation of these parameters, and their variance-covariance matrix, depends on the numerical coding used for the covariates. If an arbitrary constant is added to the covariate values, then the variance matrix is changed.

The `ftrend()` function takes the fitted model and works out an optimal constant to add to the covariate values so that the covariance matrix is approximately diagonal. The parameter estimates can then be treated as approximately independent, thus simplifying their presentation. This is particularly useful for graphical display of dose-response relationships (hence the name).

Greenland et al. (1999) originally suggested centring the covariates so that their weighted mean, using the fitted weights from the model, is zero. This heuristic criterion is improved upon by `ftrend()` which uses the same minimum information divergence criterion as used by Plummer (2003) for floating variance calculations. `ftrend()` calls `nlm()` to do the minimization and will pass optional arguments to control it.

## Value

A list with the following components

 `coef` coefficients for model with adjusted covariates. `vcov` Variance-covariance matrix of adjusted coefficients.

## Note

The "floating trend" method is an alternative to the "floating absolute risk" method, which is implemented in the function `float()`.

Martyn Plummer

## References

Greenland S, Michels KB, Robins JM, Poole C and Willet WC (1999) Presenting statistical uncertainty in trends and dose-response relations, American Journal of Epidemiology, 149, 1077-1086.

`float`