# Comparison with mgcv

#### James T. Thorson

    library(tinyVAST)
    library(pdp)  # approx = TRUE gives effects for average of other covariates
    library(lattice)
    library(visreg)
    library(mgcv)
    set.seed(101)
    options("tinyVAST.verbose" = FALSE)

`tinyVAST` is an R package for fitting vector autoregressive spatio-temporal (VAST) models using a minimal and user-friendly interface. We here show how it can replicate analysis using splines specified via `mgcv`

    # Simulate
    n_obs = 1000
    x = rnorm(n_obs)
    group = sample( x=1:5, size=n_obs, replace=TRUE )
    w = runif(n_obs, min=0, max=2)
    z = 1 + x^2 + cos((w+group/5)*2*pi) + rnorm(5)[group]
    a = exp(0.1*rnorm(n_obs))
    y = z + a + rnorm(n_obs, sd=0.2)
    Data = data.frame( x=x, y=y, w=w, z=z, group=factor(group), a=a )

    # fit model
    Formula = y ~ 1 + s(group, bs="re") + poly(x, 2, raw=TRUE) + s(w, by=group, bs="ts") # + offset(a)
    myfit = tinyVAST( data = Data,
               formula = Formula,
               control = tinyVASTcontrol( getsd=FALSE ) )

We can then compute the percent deviance explained, and confirm that it is identical to that calculated using mgcv

    # By default
    myfit$deviance_explained
    #> [1] 0.9814343

    #
    mygam_reduced = gam( Formula, data=Data ) #
    summary(mygam_reduced)$dev.expl
    #> [1] 0.9814113

We can also use the `DHARMa` package to visualize simulation residuals:

    # simulate new data conditional on fixed and random effects
    y_ir = replicate( n = 100,
               expr = myfit$obj$simulate()$y_i )

    #
    res = DHARMa::createDHARMa( simulatedResponse = y_ir,
                                observedResponse = Data$y,
                                fittedPredictedResponse = fitted(myfit) )
    plot(res)

`tinyVAST` then has a standard `predict` function:

    predict(myfit, newdata=data.frame(x=0, y=1, w=0.4, group=2, a=1) )
    #> [1] 2.977754

and this is used to compute partial-dependence plots using package `pdp`

    # compute partial dependence plot
    Partial = partial( object = myfit,
                       pred.var = c("w","group"),
                       pred.fun = \(object,newdata) predict(object,newdata),
                       train = Data,
                       approx = TRUE )

    # Lattice plots as default option
    plotPartial( Partial )

Alternatively, we can use `visreg` to visualize output, although it is disabled for CRAN vignette checks:

    visreg(myfit, xvar="group", what="p_g")
    #> Warning in plot.window(...): "what" is not a graphical parameter
    #> Warning in plot.xy(xy, type, ...): "what" is not a graphical parameter
    #> Warning in axis(side = side, at = at, labels = labels, ...): "what" is not a
    #> graphical parameter
    #> Warning in axis(side = side, at = at, labels = labels, ...): "what" is not a
    #> graphical parameter
    #> Warning in box(...): "what" is not a graphical parameter
    #> Warning in title(...): "what" is not a graphical parameter
    #> Warning in axis(side = 1, at = c(0.0833333333333333, 0.291666666666667, :
    #> "what" is not a graphical parameter

    visreg(myfit, xvar="x", what="p_g")
    #> Warning in plot.window(...): "what" is not a graphical parameter
    #> Warning in plot.xy(xy, type, ...): "what" is not a graphical parameter
    #> Warning in axis(side = side, at = at, labels = labels, ...): "what" is not a
    #> graphical parameter
    #> Warning in axis(side = side, at = at, labels = labels, ...): "what" is not a
    #> graphical parameter
    #> Warning in box(...): "what" is not a graphical parameter
    #> Warning in title(...): "what" is not a graphical parameter

    visreg(myfit, xvar="w", by="group", what="p_g")

Alternatively, we can calculate derived quantities via Monte Carlo integration of the estimated density function:

    # Predicted sample-weighted total
    integrate_output(myfit)
    #>            Estimate          Std. Error Est. (bias.correct) Std. (bias.correct)
    #>         2616.538079            7.187831         2616.538079                  NA

    # True (latent) sample-weighted total
    sum( Data$z )
    #> [1] 1606.42

Similarly, we can fit a grouped 2D spline

    # Simulate
    R = exp(-0.4 * abs(outer(1:10, 1:10, FUN="-")) )
    z = mvtnorm::rmvnorm(3, sigma=kronecker(R,R) )
    Data = data.frame( expand.grid(x=1:10, y=1:10, group=1:3), z=as.vector(t(z)))
    Data$n = Data$z + rnorm(nrow(Data), sd=0.1)
    Data$group = factor(Data$group)

    # fit model
    Formula = n ~ s(x, y, by=group)
    myfit = tinyVAST( data = Data,
               formula = Formula )

    # compute partial dependence plot
    mypartial = partial( object = myfit,
                       pred.var = c("x","y","group"),
                       pred.fun = \(object,newdata) predict(object,newdata),
                       train = Data,
                       approx = TRUE )

    # Lattice plots as default option
    plotPartial( mypartial )

    # Lattice plot of true values
    mypartial$yhat = Data$z
    plotPartial( mypartial )

We can again use `visreg` to visualize response surfaces, although it doesn’t seem possible to extract a grouped spatial term, so we here show only a single term:

    out = visreg2d( myfit, "x", "y", cond=list("group"=1), plot=FALSE )
    plot( out, main="f(x,y) for group=1")

Runtime for this vignette: 23.81 secs