Dataset: Siderastrea siderea skeletal extension

Statistical analyses were carried out using the nlme package of R 2.9.0, and Proc Mixed of SAS/STAT H software version 9.1 of SAS System for Windows. Rather than assessing and comparing average annual skeletal extension alone, as is commonly described in the literature, our goal was to also describe how rates of change in annual skeletal extension of S. siderea varied throughout the last century and amongst the forereef, backreef, and nearshore colonies. A sequence of models was fit to determine how best to describe the structural form of the data and to test the hypotheses of interest. Several models were tested, including (1) an ordinary regression model, (2) a random intercepts model with no predictors (i.e., an unconditional means model), (3) a random intercepts model that includes time as a predictor, (4) a random slopes and intercepts model in which the intercept and coefficient of time (slope) were allowed to be random, (5) a more complex version of model 3 and 4 that included level-2 predictors such as reef zone, (6) a version of model 5 that included a level-1 (residual) correlation structure, and (7) a version of model 6 that possessed a residual correlation structure without additional random effects. The variable year was ‘centered’ using a centering constant of 1967 because this minimized correlation between the random slopes and intercepts. In general, centering enhances model interpretability and improves numerical stability by increasing the likelihood that the optimization algorithm converges on the correct solution. The estimate of the slope is unchanged by centering, but the intercept will estimate the mean value of the response variable in year 1967 (rather than in year zero of the uncentered model). The role of centering in mixed effects models is discussed in greater detail in O’Connor et al. (2007). Akaike Information Criterion (AIC) was used to identify the best-fit model. AIC provides a measure of the explanatory power of a model discounted by the number of parameters that contributed to its construction; a lower value indicates a better fitting model. Of all the models that were fit, the random intercepts model with an ARMA (1, 1) correlation structure for the residuals yielded the lowest AIC. An ARMA (1, 1) correlation structure combines an autoregressive model of order 1 with a moving average model of order 1. The appropriateness of the ARMA (1, 1) structure was also indicated by patterns observed in plots of the autocorrelation and partial autocorrelation functions of the residuals.

BCO-DMO Processing Notes
- Generated from original files Siderastrea siderea skeletal extension.csv" contributed by Karl Castillo
- Parameter names edited to conform to BCO-DMO naming convention found at Choosing Parameter Name