# Predict gravity model predict method for class "gravity" ```r ## S3 method for class 'gravity' predict( object, newdata, groups = NULL, back.transform = c("none", "simple", "Miller", "Naihua"), ... ) ``` ## Arguments - `object`: Object of class gravity - `newdata`: New data used for obtaining the predictions, can be a data.frame or nffGroupedData - `groups`: Grouping factor acting as random effect. If used, must match levels used in model, otherwise leave it null and do not convert to groupedData - `back.transform`: Method to back transform data, default is none and log predictions will be returned. - `...`: Arguments passed to predict.lme or predict.lm ## Returns Vector of model predictions ## Details Please note that the entire gravity equation is log transformed so, your parameter space is on a log scale, not just y. This means that for a meaningful prediction the "newdata" also needs to be on a log scale. For the back.transform argument, the simple back-transform method uses the form exp(y-hat)0.5*variance whereas Miller uses exp(sigma)*0.5 as the multiplicative bias factor. Naihua regresses y~exp(y-hat) with no intercept and uses the resulting coefficient as the multiplicative bias factor. The Naihua method is intended for results with non-normal errors. You can check the functional form by simply plotting y (non-transformed) against the fit. The default is to output the log scaled predictions. ## Examples ```r library(nlme) data(ralu.model) back.transform <- function(y) exp(y + 0.5 * stats::var(y, na.rm=TRUE)) rmse = function(p, o){ sqrt(mean((p - o)^2)) } x = c("DEPTH_F", "HLI_F", "CTI_F", "cti", "ffp") sidx <- sample(1:nrow(ralu.model), 100) train <- ralu.model[sidx,] test <- ralu.model[-sidx,] # Specify constrained gravity model ( gm <- gravity(y = "DPS", x = x, d = "DISTANCE", group = "FROM_SITE", data = train, ln = FALSE) ) ( p <- predict(gm, test[,c(x, "DISTANCE")]) ) rmse(back.transform(p), back.transform(ralu.model[,"DPS"][-sidx])) # WIth model sigma-based back transformation ( p <- predict(gm, test[,c(x, "DISTANCE")], back.transform = "simple") ) ( p <- predict(gm, test[,c(x, "DISTANCE")], back.transform = "Miller") ) ( p <- predict(gm, test[,c(x, "DISTANCE")], back.transform = "Naihua") ) # Using grouped data test <- nlme::groupedData(stats::as.formula(paste(paste("DPS", 1, sep = " ~ "), "FROM_SITE", sep = " | ")), data = test[,c("DPS", "FROM_SITE", x, "DISTANCE")]) ( p <- predict(gm, test, groups = "FROM_SITE") ) ( y.hat <- back.transform(ralu.model[,"DPS"][-sidx]) ) na.idx <- which(is.na(p)) rmse(back.transform(p)[-na.idx], y.hat[-na.idx]) # Specify unconstrained gravity model (generally, not recommended) ( gm <- gravity(y = "DPS", x = x, d = "DISTANCE", group = "FROM_SITE", data = train, ln = FALSE, constrained=TRUE) ) ( p <- predict(gm, test[,c(x, "DISTANCE")]) ) rmse(back.transform(p), back.transform(ralu.model[,"DPS"][-sidx])) ``` ## References Miller, D.M. (1984) Reducing Transformation Bias in Curve Fitting The American Statistician. 38(2):124-126 Naihua, D. (1983) Smearing Estimate: A Nonparametric Retransformation Method Journal of the American Statistical Association, 78(383):605–610. ## Author(s) Jeffrey S. Evans and Melanie A. Murphy

predict.gravity function