How to plot surface fit through 3D data in R?

Question

I have a 3D scatter plot that renders like this:

The 3D dataset is very big, so I can't include it here. One can try and answer this using the standard datasets like mtcars or iris.

My attempt to plot this 3D scatterplot:

x <- rbind(A_0,A_1,A_2,A_3) 
fig1 <- x %>% plot_ly(x= ~x,y=~y,z = ~z, color= ~key,type="scatter3d", size = 0.5)
fig1

A_0, A_1, A_2, A_3 are different 3*n dataframes which are combined together using rbind and differentiated by using the key included in each dataframe

I tried fitting the surface by various methods like add_surface(), add_trace(), changing the type to 'mesh3D'

But, the resultant surface fit is not what I want, I need a smooth surface fitting through this scatter data. The error I am getting is this: z is not a numeric matrix.

Is there any better way of fitting the surface, what am I missing here?

P.S. I would prefer rendering the plot with ggplot(), plot_ly(), ggplotly().

user_8206434 · Answer

You could fit a model first using something like gam() and then plot the predictions. First, we can fit the GAM to the data. In this case, hp and wtare the two independent variables (i.e., the x and y axes of the chart above). qsec is the variable plotted on the z-axis and is the dependent variable in the model.

data(mtcars)
library(mgcv)
mod <- gam(qsec ~ te(hp) + te(wt) + ti(hp, wt), data=mtcars)

Next, we need to make some predictions for the model at different combinations of hp and wt. The easiest way to do this is to make a sequence of values for each variable that goes from their minima to their maxima. This is what the commands below do. It makes a sequence of 25 evenly spaced values going from the minimum to the maximum of each independent variable.

hp.seq <- seq(min(mtcars$hp, na.rm=TRUE), max(mtcars$hp, na.rm=TRUE), length=25)
wt.seq <- seq(min(mtcars$wt, na.rm=TRUE), max(mtcars$wt, na.rm=TRUE), length=25)

Next, we can make a function that will generate predictions. Because we are going to use outer() below, we should have the function take two inputs and x and a y. The x-y pairs we are going to pass in are the values of hp and wt used for the predictions. The function makes a data frame that has one observation and two variables - hp and wt. It uses that new data frame to generate a single prediction from the model using the predict() function.

predfun <- function(x,y){
  newdat <- data.frame(hp = x, wt=y)
  predict(mod, newdata=newdat)
}

Next, we apply that prediction function to the sequences of data we made above. We use outer() the outer-product function to make a 25x25 matrix of predicted values for every combination of hp.seq and wt.seq. Wrapping predfun in Vectorize() prevents errors about replacement length problems.

fit <- outer(hp.seq, wt.seq, Vectorize(predfun))

Finally, we can put everything together in plot_ly. We use add_marker() to add the points and add_surface to add the predictions.

plot_ly() %>% 
  add_markers(x = ~mtcars$hp, y=mtcars$wt, z=mtcars$qsec) %>% 
  add_surface(x = ~hp.seq, y = ~wt.seq, z = t(fit))

How to plot surface fit through 3D data in R?

1 Answers