Stop extrapolation when forecasting using two variables

Question

After choosing a model, my best model has two continuous variables with the term interaction.

My data is as follows:

df<-structure(list(Height_RR = c(1.09861228866811, -0.143100843640673, -0.990398704027877, -0.990398704027877, 0.0800427076735365, 0.916290731874155, 1.04982212449868, 0.430782916092454, 0.575364144903562, 0.0953101798043248, -0.405465108108164, 0.132489183046079, 0.117783035656383, 1.04982212449868, -0.916290731874155, 1.20397280432594, -0.356674943938732, 0.287682072451781, -0.356674943938732, 0.287682072451781, -0.356674943938732, 0.287682072451781, -0.318387168583869, -0.318387168583869, -0.318387168583869, -0.356674943938732, -0.393042588109607, -0.485507815781701, -0.405465108108164, -0.441832752279039, 0.42744401482694, 0.510825623765991, 1.04982212449868, 0.847297860387204, -0.356674943938732), CWD = c(-173.850331373113, -1063.65743501896, -1152.77456298827, -1200.14062275391, -1191.1454796875, -154.366681649412, -160.237513231871, -148.917478721144, -655.155005728001, -1081.17124999999, -192.437500000001, -664.538976252586, -540.755930464004, -230.945841787738, -632.705104201392, -159.376784299775, -686.792144988283, -686.792144988283, -686.792144988283, -686.792144988283, -686.792144988283, -686.792144988283, -681.113600988285, -681.113600988285, -681.113600988285, -203.026923561875, -32.6625046554887, -499.426709860029, -190.121159505859, -871.942483370128, -988.569593505865, -248.140000031999, -165.422048285183, -165.422048285183, -165.422048285183), yi = c(0.201673327454905, 0.374187870755073, -1.26459742614237, -3.4162352590267, -1.20397280432594, 0.943371690476826, 1.26291533995939, 0.551099522903931, 0.506212624114382, 1.62113395219729, -0.272257602126149, 0.345151698858396, 0.104290175606367, 4.56284362374715, 0.532233017860013, 0.697137826765664, -1.01160091167848, -1.07044141170141, 0.646627164925052, -0.519875459285909, -0.646627164925052, -0.519875459285909, -0.424883193965266, 0.074107972153722, 0.074107972153722, 0.693147180559945, 0.0707340508073709, 0.358554516423803, -0.682820066404096, -0.638455438611528, 0.410070448690588, 1.11317243999944, 1.26976054486394, 1.45111186119636, 1.44238382777093)), .Names = c("Height_RR", "CWD", "yi"), row.names = c(1L, 2L, 3L, 4L, 5L, 6L, 7L, 8L, 10L, 11L, 12L, 13L, 14L, 15L, 16L, 17L, 19L, 20L, 21L, 22L, 23L, 24L, 25L, 26L, 27L, 28L, 29L, 30L, 31L, 33L, 34L, 35L, 36L, 37L, 38L), class = "data.frame") 

And my estimates of the model parameters are as follows:

  estimate se zval pval ci.lb ci.ub intrcpt 1.1422 0.3862 2.9575 0.0031 0.3852 1.8991 ** Height_RR 0.3412 0.1488 2.2925 0.0219 0.0495 0.6328 * CWD 0.0014 0.0006 2.2698 0.0232 0.0002 0.0026 * Height_RR:CWD -0.0006 0.0002 -3.0161 0.0026 -0.0009 -0.0002 ** 

I want to display predictions from this result using a figure where both x and y axes are continuous predictor variables and the predicted value is represented by a color ramp. Using this code, I get the following figure

 library(ggplot2) new.data<-expand.grid(Height_RR=seq(min(df$Height_RR),max(df$Height_RR),length.out = 20), CWD=seq(min(df$CWD,na.rm = T),max(df$CWD,na.rm = T),length.out = 20)) new.data$yi<-(new.data$Height_RR*0.3412)+1.1422+(0.0014*new.data$CWD)+((new.data$CWD*new.data$Height_RR)*0.0006) ggplot(new.data,aes(x=Height_RR,y=CWD,fill=yi))+geom_raster()+scale_fill_continuous(low="light grey",high="black") 

However, I do not have data for all regions of this plot, and therefore I extrapolate this model. The minimum convex hull and the points in the figure below show where my data is

My questions:

• Is there a way to create a dataframe to limit my forecasts to the region in which I have data (e.g. inside a polygon)?
• If not, is there a better way to display the interactions between two continuous variables?

Answer 1

Here is the idea, I hope that everything is correct.

 # Create a convex hull of the points in df and turn that into a polygon of class SpatialPolygons: ch <- chull(df$Height_RR, df$CWD) poly.df <- df[c(ch, ch[1]),] poly <- SpatialPolygons(list(Polygons(list(Polygon(as.matrix(poly.df[,1:2]))),1))) # Create a SpatialPointsDataFrame with new.data: library(sp) new.data.poly <- new.data coordinates(new.data.poly) <- ~Height_RR+CWD # Extract the points in new.data which are covered by the polygon: new.data$inp <- over(new.data.poly, poly) new.data <- new.data[complete.cases(new.data),] # Calculate yi as you did: new.data$yi<-(new.data$Height_RR*0.3412) + 1.1422 + (0.0014*new.data$CWD) + ((new.data$CWD*new.data$Height_RR)*0.0006) # Plot: ggplot(new.data, aes(x=Height_RR,y=CWD,fill=yi)) + geom_raster() + scale_fill_continuous(low="light grey",high="black") 

Answer 2

You can use dismo :: convHull to evaluate and predict (determine if data is inside) a convex corpus. You can then use this to mask cells that fall outside the enclosure in your current plot.

Answer 3

Are you looking for something like this?

 ggplot(df,aes(x=Height_RR,y=CWD))+geom_point(aes(col=yi)) 

Graph result