[R] mgcv: beta coefficient and 95%CI

[Simon Wood]

Isn't the point here that they used smooths for the other terms but a linear 
effect (or several) for (lagged) visibility. So you do have a beta in this 
case, and the gam summary would tell you what it is estimated to be and what 
the associated standard error is. The 'coef' and 'vcov' functions also allow 
you to extract this information from the fitted model summary.

The model you have posted is different however, in that you have replaced the 
linear term with a smooth, so there is no single beta and the interpretation 
is therefor different.

On Wednesday 23 February 2011 14:40, clc wrote:
> In one of the papers...
>
> We developed core models with a generalized additive Poisson regression
> allowing for over-dispersion in the model (Wood, 2006). For each mortality
> outcome, variations in seasonality, trends, mean temperature, and mean
> humidity of current and previous days (lag 0–1) were fitted with penalized
> cubic regression splines. Dummy variables were used to control the
> variations for days of the week, holidays, and influenza epidemics. We
> added a dummy variable for the 2003 severe acute respiratory syndrome
> (SARS) epidemic. We chose 4 degrees of freedom (df) per year for smoothing
> function of the trends and 3 df for temperature and humidity. The choice of
> df for each smoothing function in the core models was made on the basis of
> observed residual autocorrelations using partial autocorrelation function
> (PACF). For the core models fitted to the mortality data, time variant
> confounding factors were considered as adequately controlled if absolute
> values of PACF coefficients were <0.1 for the first two lag days and there
> were no systematic patterns in the PACF plots.
>
> Following the construction of an adequate core model for each mortality
> outcome, we entered visibility as a linear term into the regression model
> and examined the effects of visibility on mortality for single day lags 0–5
> days, lag 0–1, and distributed lag 0–4 days ([Schwartz, 2000] and
> [Zanobetti et al., 2000]). The distributed lag effect take into account the
> possibility that visibility can affect deaths occurring on the same day and
> on several subsequent days. The net effect of visibility was the sum of the
> effect estimates for all six days. We expressed the effect of visibility as
> the percentage change in daily mortality with a decrease in the
> interquartile range (IQR) of visibility as 100%×IQR×β, where β is the
> estimated Poisson regression coefficient, and referred to as the excess
> risk (ER%).
>
>
>
> in one of the figures, they reported "Estimated excess risks (ER%) for
> daily mortality and associated 95% confidence intervals per interquartile
> range decrease in visibility (6.5 km) at single lags 0–5, mean lag 0–1
> (0–1) and distributed lag (DL) for lag 0–4 days"
>
>
> What do they mean??! Thanks a lot!

-- 
> Simon Wood, Mathematical Sciences, University of Bath, Bath, BA2 7AY UK
> +44 1225 386603  www.maths.bath.ac.uk/~sw283