eric-pedersen

---
title: "Testing $R^2$ predictions varying link and functional response"
author: "Eric Pedersen"
date: '2022-07-20'
output: html_document
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE, warning = FALSE)
```

eric-pedersen

#
# This is a Shiny web application. You can run the application by clicking
# the 'Run App' button above.
#
# Find out more about building applications with Shiny here:
#
#    http://shiny.rstudio.com/
#

library(shiny)

eric-pedersen

library(mgcv)
set.seed(3);n <- 400

############################################
## First example: simulated Tweedie model...
############################################

dat <- gamSim(1,n=n,dist="poisson",scale=.2)
dat$y <- rTweedie(exp(dat$f),p=1.3,phi=.5) ## Tweedie response
b <- gam(y~s(x0)+s(x1)+s(x2)+s(x3),family=tw(),

eric-pedersen

#Create an explicit binomially distributed set of numbers
n = 1000
frac = 0.9
x = rep(c(1,0),times = c(n*frac, n*(1-frac)))

#Fit a Gaussian model and a binomial model to the same data
gauss_mod = glm(x~1,family = gaussian)
binom_mod = glm(x~1, family= binomial)

#Compare AIC

eric-pedersen

library(mgcv)

#creating data for the smooth matrix and for predictions
inner_range = c(1900, 2000)
outer_range = c(1850, 2050)

dat = data.frame(year = seq(inner_range[1],inner_range[2],length=500))
pred = data.frame(year = seq(outer_range[1],outer_range[2],length=500))

eric-pedersen

library(mgcv)

#creating data for the smooth matrix and for predictions
inner_range = c(1900, 2000)
outer_range = c(1850, 2050)

dat = data.frame(year = seq(inner_range[1],inner_range[2],length=500))
pred = data.frame(year = seq(outer_range[1],outer_range[2],length=500))

eric-pedersen

# extrapolating into the future with B-splines
#  based on code in ?smooth.construct.bs.smooth.spec

library(mgcv)

# annual diameter of women’s skirts at the hem 1866 to 1911
# Hipel and McLeod, 1994
skirts <- scan("http://robjhyndman.com/tsdldata/roberts/skirts.dat",skip=5)
skirtseries <- data.frame(year=1866:1911, diam=skirts)

eric-pedersen

library(mgcv)

# annual diameter of women’s skirts at the hem 1866 to 1911
# Hipel and McLeod, 1994
skirts <- scan("http://robjhyndman.com/tsdldata/roberts/skirts.dat",skip=5)
skirtseries <- data.frame(year=1866:1911, diam=skirts)

# prediction grid
pd <- data.frame(year=seq(1864, 1960, by=1))

eric-pedersen

library(dplyr)
library(mgcv)

#You need the multivariate normal RNG from the MASS package
mvrnorm = MASS::mvrnorm

# Functions to calculate the 1st and 2nd derivatives of a given time series with a given step size
# Uses two-point approximations for both 1st and 2nd derivs.
calc_1st_deriv = function(y,delta) (lead(y,1) - lag(y,1))/(2*delta)
calc_2nd_deriv = function(y,delta) (lead(y,1) + lag(y,1)-2*y)/delta^2

eric-pedersen

library(dplyr)
library(tidyr)
library(ggplot2)
library(mgcv)
library(purrr)
nreps = 100
#Simulate data from a sinusoidal function. Point of equality should be at
#0/12 (or 0.5/12.5, or 1/13, etc.) by design.
sims = crossing(x= 1:12, rep = 1:nreps)%>%
  mutate(y= 4*sin(2*pi*x/12)+rnorm(nreps,0,1))