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Copy pathDelayed Demand Supplemental Code.R
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Delayed Demand Supplemental Code.R
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# initializing ----
library(data.table)
library(nlme)
library(AICcmodavg)
library(nls.multstart)
library(ggplot2)
library(beezdemand)
library(plot3D)
library(gridExtra)
#
# testAIC <- c(0, 1, 2, 3, 20, 20, 20, 20, 20, 20, 20)
# # (testAIC-min(testAIC))
# exp(-(1/2) * (testAIC-min(testAIC))) / sum(exp(-(1/2) * (testAIC-min(testAIC))))
# # exp(-(1/2) * (paperAIC-min(paperAIC))) / sum(exp(-(1/2) * (paperAIC-min(paperAIC))))
# use mean k above all points for determining k
# setting the seed
set.seed(09264)
### Below is not run but included for transparency, data organization process----
## fagerstrom cleaner----
# fagerstrom <- function(x){
# fcase(
# x %in% c("No", "All others", "After 60 minutes", "10 or less"), 0,
# x %in% c("Yes","The first one in the morning", "30-60 minutes", "20-Nov"), 1,
# x %in% c("6-30 minutes", "21-30"), 2,
# x %in% c("Within 5 minutes", "31 or more"), 3
# )
# }
## data import ----
#
#
# allData <- fread("delayeddemandalldata.csv", na.strings = "")
# allData <- allData[-c(1:2),]
# allData$FTNDnum <- apply(allData[, lapply(.SD, fagerstrom), .SDcols = grepl("FTND", names(allData))], 1, sum)
# allData[, id := paste0("A", 1:nrow(allData))]
# cptData <- allData[, c(grep("id|cpt|FTNDnum", names(allData))), with = FALSE]
#
#
#
#
# longData <- melt(cptData, id.vars = c("id", "FTNDnum"), value.name = "z")[order(id, variable)]
# longData[, levels(variable)]
#
# delays <- c(round(5/60, 4), 6, 24, 7*24, 30*24, 90*24, 365*24, 24*365*5)
# prices <- c(.01, .03, .06, .13, .25, .5, 1, 2, 4, 8)
#
# longData[, y := rep(delays, each = length(prices), length(unique(id)))]
# longData[, x := rep(prices, length(unique(id)) * length(delays))]
# longData[, z := as.numeric(z)]
# longData[, .N, by = id]$N
# cleanLong <- longData[complete.cases(longData$z)]
## Removing points above 200 ----
# badNames <- cleanLong[z > 200, unique(id)]
# length(badNames)
# cleanLong <- cleanLong[!id %in% badNames]
#
## Systematic
# systematic3D <- function(data){
# set1 <- data[x == min(x) & y == min(y), z, by = id]$id[which(data[x == min(x) & y == min(y), z, by = id]$z -
# data[x == max(x) & y == max(y), z, by = id]$z < 0)]
# set2 <- data[x == min(x) & y == min(y), z, by = id]$id[which(data[x == min(x) & y == min(y), z, by = id]$z -
# data[x == min(x) & y == max(y), z, by = id]$z < 0)]
# set3 <- data[x == min(x) & y == min(y), z, by = id]$id[which(data[x == min(x) & y == min(y), z, by = id]$z -
# data[x == max(x) & y == min(y), z, by = id]$z < 0)]
# return(((list(set1, set2, set3))))
# }
# length(Reduce(intersect, systematic3D(longData)))
#
# lapply(systematic3D(longData), length)
# length(unique(unlist(systematic3D(longData))))
# missingDataNames <- cleanLong[, .N, by = id][which(cleanLong[, .N, by = id]$N< 80), id]
# cleanLong <- cleanLong[!id %in% missingDataNames]
# doubleBadNames <- unlist(systematic3D(cleanLong))
# length(doubleBadNames)
# cleanLong <- cleanLong[!id %in% doubleBadNames]
# cleanLong[, unique(id)]
#
# write.csv(allData[id %in% cleanLong[, unique(id)], .SD, .SDcols = c(grepl("Duration|Marital|Income|Dependents|Age|Race|Race_7_TEXT|Education|Employment|FTNDnum", names(allData)))],
# "delayeddemanddemo.csv")
# write.csv(cleanLong,
# "delayeddemandcpt.csv")
#
# durations <- function(x){
# return(c(range(x),
# mean(x),
# median(x)))
# }
#
# allData[id %in% cleanLong[, unique(id)], .SD,
# .SDcols = c(grepl("Duration|Marital|Income|Dependents|Age|Race|Race_7_TEXT|Education|Employment|FTNDnum", names(allData)))][
# , durations(as.numeric(`Duration (in seconds)`))/60
# ]
#
#
# cleanLong[, length(unique(id))]
# Data analysis begins ----
cleanLong <- fread("delayeddemandcpt.csv")
GetKZ <- function (dat, mnrange = TRUE) {
if (mnrange) {
dat1 <- aggregate(z ~ x, dat, mean)
(log10(max(dat1$z[dat1$z > 0], na.rm = TRUE)) - log10(min(dat1$z[dat1$z >
0], na.rm = TRUE)))
}
else {
(log10(max(dat$z[dat$z > 0], na.rm = TRUE)) - log10(min(dat$z[dat$z >
0], na.rm = TRUE)))
}
}
cleanLong[, k := GetKZ(data.frame(z, x))]
# 2D demand and discounting ----
# base demand ----
expDemand <- nls_multstart(z ~ (10^(q0) * 10^(k *(exp(-10^(alpha)*10^(q0)*x)-1))), data = subset(cleanLong, y == min(y)) ,
iter = 250,
start_lower = c(q0 = .1, alpha = -4),
start_upper = c(q0 = 2, alpha = 4))
expDemandCovGNLS <- gnls(z ~ (10^(q0) * 10^(k *(exp(-10^(alpha)*10^(q0)*x)-1))),
data = subset(cleanLong, y == min(y)),
params = list(q0 ~ scale(FTNDnum),
alpha ~ scale(FTNDnum)
),
start = list(fixed = c(coef(expDemand)[1], 0, coef(expDemand)[2], 0)),
verbose = 2,
control = list(msMaxIter = 50000,
niterEM = 5000,
maxIter = 5000,
pnlsTol = .01,
tolerance = .5,
apVar = T,
minScale = .0000001,
opt = "optim"), na.action = na.omit)
expDemandMLM <- nlme(z ~ (10^(q0) * 10^(k *(exp(-10^(alpha)*10^(q0)*x)-1))),
data = subset(cleanLong, y == min(y)),
fixed = list(q0 ~ 1,
alpha ~ 1),
random = list(pdSymm(q0 + alpha ~ 1)),
start = list(fixed = coef(expDemand)),
groups = ~id,
method = "ML",
verbose = 2,
control = list(msMaxIter = 50000,
niterEM = 5000,
maxIter = 5000,
pnlsTol = .01,
tolerance = .01,
apVar = T,
minScale = .0000001,
opt = "optim"), na.action = na.omit)
expDemandCovMLM <- nlme(z ~ (10^(q0) * 10^(k *(exp(-10^(alpha)*10^(q0)*x)-1))),
data = subset(cleanLong, y == min(y)),
fixed = list(q0 ~ scale(FTNDnum),
alpha ~ scale(FTNDnum)),
random = list(pdSymm(q0 + alpha ~ 1)),
start = list(fixed = coef(expDemandCovGNLS)),
groups = ~id,
method = "ML",
verbose = 2,
control = list(msMaxIter = 50000,
niterEM = 5000,
maxIter = 5000,
pnlsTol = .01,
tolerance = .01,
apVar = T,
minScale = .0000001,
opt = "optim"), na.action = na.omit)
summary(expDemandCovMLM)
round(summary(expDemandCovMLM)$tTable, 3)
# ----
exp.5Demand <- nls_multstart(z ~ (10^(q0) * 10^((k+.5) *(exp(-10^(alpha)*10^(q0)*x)-1))), data = subset(cleanLong, y == min(y)) ,
iter = 250,
start_lower = c(q0 = .1, alpha = -4),
start_upper = c(q0 = 2, alpha = 4))
exp.5DemandCovGNLS <- gnls(z ~ (10^(q0) * 10^((k+.5) *(exp(-10^(alpha)*10^(q0)*x)-1))),
data = subset(cleanLong, y == min(y)),
params = list(q0 ~ scale(FTNDnum),
alpha ~ scale(FTNDnum)
),
start = list(fixed = c(coef(exp.5Demand)[1], 0, coef(exp.5Demand)[2], 0)),
verbose = 2,
control = list(msMaxIter = 50000,
niterEM = 5000,
maxIter = 5000,
pnlsTol = .01,
tolerance = .5,
apVar = T,
minScale = .0000001,
opt = "optim"), na.action = na.omit)
exp.5DemandMLM <- nlme(z ~ (10^(q0) * 10^((k+.5) *(exp(-10^(alpha)*10^(q0)*x)-1))),
data = subset(cleanLong, y == min(y)),
fixed = list(q0 ~ 1,
alpha ~ 1),
random = list(pdSymm(q0 + alpha ~ 1)),
start = list(fixed = coef(exp.5Demand)),
groups = ~id,
method = "ML",
verbose = 2,
control = list(msMaxIter = 50000,
niterEM = 5000,
maxIter = 5000,
pnlsTol = .01,
tolerance = .01,
apVar = T,
minScale = .0000001,
opt = "optim"), na.action = na.omit)
exp.5DemandCovMLM <- nlme(z ~ (10^(q0) * 10^((k+.5) *(exp(-10^(alpha)*10^(q0)*x)-1))),
data = subset(cleanLong, y == min(y)),
fixed = list(q0 ~ scale(FTNDnum),
alpha ~ scale(FTNDnum)),
random = list(pdSymm(q0 + alpha ~ 1)),
start = list(fixed = coef(exp.5DemandCovGNLS)),
groups = ~id,
method = "ML",
verbose = 2,
control = list(msMaxIter = 50000,
niterEM = 5000,
maxIter = 5000,
pnlsTol = .01,
tolerance = .01,
apVar = T,
minScale = .0000001,
opt = "optim"), na.action = na.omit)
summary(expDemandCovMLM)
round(summary(exp.5DemandCovMLM)$tTable, 3)
# ----
# Rachlin Demand ----
rachlinDemand <- nls_multstart(z ~ 10^q0/(1 + 10^b * x ^ s), data = subset(cleanLong, y == min(y)) ,
iter = 250,
start_lower = c(q0 = .1, b = -4, s = .1),
start_upper = c(q0 = 2, b = 4, s = 4))
rachlinDemandCovGNLS <- gnls(z ~ 10^q0/(1 + 10^b * x ^ s),
data = subset(cleanLong, y == min(y)),
params = list(q0 ~ scale(FTNDnum),
b ~ scale(FTNDnum),
s ~ scale(FTNDnum)
),
start = list(fixed = c(coef(rachlinDemand)[1], 0, coef(rachlinDemand)[2], 0, coef(rachlinDemand)[3], 0)),
verbose = 2,
control = list(msMaxIter = 50000,
niterEM = 5000,
maxIter = 5000,
pnlsTol = .01,
tolerance = .05,
apVar = T,
minScale = .0000001,
opt = "optim"), na.action = na.omit)
rachlinDemandMLM <- nlme(z ~ 10^q0/(1 + 10^b * x ^ s),
data = subset(cleanLong, y == min(y)),
fixed = list(q0 ~ 1,
b ~ 1,
s ~ 1
),
random = list(pdSymm(q0 + b + s~ 1)),
start = list(fixed = coef(rachlinDemand)),
groups = ~id,
method = "ML",
verbose = 2,
control = list(msMaxIter = 50000,
niterEM = 5000,
maxIter = 5000,
pnlsTol = .01,
tolerance = .5,
apVar = T,
minScale = .0000001,
opt = "optim"), na.action = na.omit)
rachlinDemandCovMLM <- nlme(z ~ 10^q0/(1 + 10^b * x ^ s),
data = subset(cleanLong, y == min(y)),
fixed = list(q0 ~ scale(FTNDnum),
b ~ scale(FTNDnum),
s ~ scale(FTNDnum)
),
random = list(pdSymm(q0 + b + s~ 1)),
start = list(fixed = coef(rachlinDemandCovGNLS)),
groups = ~id,
method = "ML",
verbose = 2,
control = list(msMaxIter = 50000,
niterEM = 5000,
maxIter = 5000,
pnlsTol = .01,
tolerance = .5,
apVar = T,
minScale = .0000001,
opt = "optim"), na.action = na.omit)
summary(rachlinDemandCovMLM)
round(summary(rachlinDemandCovMLM)$tTable, 3)
anova(exp.5DemandCovMLM, rachlinDemandCovMLM)
anova(expDemandCovMLM, exp.5DemandCovMLM, rachlinDemandCovMLM)
anova(exp.5DemandMLM, rachlinDemandMLM)
anova(expDemandMLM, exp.5DemandMLM, rachlinDemandMLM)
# Rachlin delay ----
rachlinDelay <- nls_multstart(z ~ 10^q0/(1 + 10^b * y ^ s), data = subset(cleanLong, x == min(x)) ,
iter = 250,
start_lower = c(q0 = .1, b = -4, s = .1),
start_upper = c(q0 = 2, b = 4, s = 4))
rachlinDelayCovGNLS <- gnls(z ~ 10^q0/(1 + 10^b * y ^ s),
data = subset(cleanLong, x == min(x)),
params = list(q0 ~ scale(FTNDnum),
b ~ scale(FTNDnum),
s ~ scale(FTNDnum)
),
start = list(fixed = c(coef(rachlinDelay)[1], 0, coef(rachlinDelay)[2], 0, coef(rachlinDelay)[3], 0)),
verbose = 2,
control = list(msMaxIter = 50000,
niterEM = 5000,
maxIter = 5000,
pnlsTol = .01,
tolerance = .5,
apVar = T,
minScale = .0000001,
opt = "optim"), na.action = na.omit)
rachlinDelayMLM <- nlme(z ~ 10^q0/(1 + 10^b * y ^ s),
data = subset(cleanLong, x == min(x)),
fixed = list(q0 ~ 1,
b ~ 1,
s ~ 1
),
random = list(pdSymm(q0 + b + s~ 1)),
start = list(fixed = coef(rachlinDelay)),
groups = ~id,
method = "ML",
verbose = 2,
control = list(msMaxIter = 50000,
niterEM = 5000,
maxIter = 5000,
pnlsTol = .01,
tolerance = 1.1,
apVar = T,
minScale = .0000001,
opt = "optim"), na.action = na.omit)
rachlinDelayCovMLM <- nlme(z ~ 10^q0/(1 + 10^b * y ^ s),
data = subset(cleanLong, x == min(x)),
fixed = list(q0 ~ scale(FTNDnum),
b ~ scale(FTNDnum),
s ~ scale(FTNDnum)
),
random = list(pdSymm(q0 + b + s~ 1)),
start = list(fixed = coef(rachlinDelayCovGNLS)),
groups = ~id,
method = "ML",
verbose = 2,
control = list(msMaxIter = 50000,
niterEM = 5000,
maxIter = 5000,
pnlsTol = .01,
tolerance = .5,
apVar = T,
minScale = .0000001,
opt = "optim"), na.action = na.omit)
summary(rachlinDelayCovMLM)
round(summary(rachlinDelayCovMLM)$tTable, 3)
# Exponentiated Delay ----
expDelay <- nls_multstart(z ~ (10^(q0) * 10^(k *(exp(-10^(alpha)*10^(q0)*y)-1))), data = subset(cleanLong, x == min(x)) ,
iter = 250,
start_lower = c(q0 = .1, alpha = -4),
start_upper = c(q0 = 2, alpha = 4))
expDelayCovGNLS <- gnls(z ~ (10^(q0) * 10^(k *(exp(-10^(alpha)*10^(q0)*y)-1))),
data = subset(cleanLong, x == min(x)),
params = list(q0 ~ scale(FTNDnum),
alpha ~ scale(FTNDnum)
),
start = list(fixed = c(coef(expDelay)[1], 0, coef(expDelay)[2], 0)),
verbose = 2,
control = list(msMaxIter = 50000,
niterEM = 5000,
maxIter = 5000,
pnlsTol = .01,
tolerance = .5,
apVar = T,
minScale = .0000001,
opt = "optim"), na.action = na.omit)
expDelayMLM <- nlme(z ~ (10^(q0) * 10^(k *(exp(-10^(alpha)*10^(q0)*y)-1))),
data = subset(cleanLong, x == min(x)),
fixed = list(q0 ~ 1,
alpha ~ 1),
random = list(pdSymm(q0 + alpha ~ 1)),
start = list(fixed = coef(expDelay)),
groups = ~id,
method = "ML",
verbose = 2,
control = list(msMaxIter = 50000,
niterEM = 5000,
maxIter = 5000,
pnlsTol = .01,
tolerance = .01,
apVar = T,
minScale = .0000001,
opt = "optim"), na.action = na.omit)
expDelayCovMLM <- nlme(z ~ (10^(q0) * 10^(k *(exp(-10^(alpha)*10^(q0)*y)-1))),
data = subset(cleanLong, x == min(x)),
fixed = list(q0 ~ scale(FTNDnum),
alpha ~ scale(FTNDnum)),
random = list(pdSymm(q0 + alpha ~ 1)),
start = list(fixed = coef(expDelayCovGNLS)),
groups = ~id,
method = "ML",
verbose = 2,
control = list(msMaxIter = 50000,
niterEM = 5000,
maxIter = 5000,
pnlsTol = .01,
tolerance = .01,
apVar = T,
minScale = .0000001,
opt = "optim"), na.action = na.omit)
summary(expDelayCovMLM)
round(summary(expDelayCovMLM)$tTable, 3)
expDelayCovMLM <- nlme(z ~ (10^(q0) * 10^(k *(exp(-10^(alpha)*10^(q0)*y)-1))),
data = subset(cleanLong, x == min(x)),
fixed = list(q0 ~ scale(FTNDnum),
alpha ~ scale(FTNDnum)),
random = list(pdSymm(q0 + alpha ~ 1)),
start = list(fixed = coef(expDelayCovGNLS)),
groups = ~id,
method = "ML",
verbose = 2,
control = list(msMaxIter = 50000,
niterEM = 5000,
maxIter = 5000,
pnlsTol = .01,
tolerance = .01,
apVar = T,
minScale = .0000001,
opt = "optim"), na.action = na.omit)
summary(expDelayCovMLM)
round(summary(expDelayCovMLM)$tTable, 3)
exp.5Delay <- nls_multstart(z ~ (10^(q0) * 10^((k+.5) *(exp(-10^(alpha)*10^(q0)*y)-1))), data = subset(cleanLong, x == min(x)) ,
iter = 250,
start_lower = c(q0 = .1, alpha = -4),
start_upper = c(q0 = 2, alpha = 4))
exp.5DelayCovGNLS <- gnls(z ~ (10^(q0) * 10^((k+.5) *(exp(-10^(alpha)*10^(q0)*y)-1))),
data = subset(cleanLong, x == min(x)),
params = list(q0 ~ scale(FTNDnum),
alpha ~ scale(FTNDnum)
),
start = list(fixed = c(coef(exp.5Delay)[1], 0, coef(exp.5Delay)[2], 0)),
verbose = 2,
control = list(msMaxIter = 50000,
niterEM = 5000,
maxIter = 5000,
pnlsTol = .01,
tolerance = .5,
apVar = T,
minScale = .0000001,
opt = "optim"), na.action = na.omit)
exp.5DelayMLM <- nlme(z ~ (10^(q0) * 10^((k+.5) *(exp(-10^(alpha)*10^(q0)*y)-1))),
data = subset(cleanLong, x == min(x)),
fixed = list(q0 ~ 1,
alpha ~ 1),
random = list(pdSymm(q0 + alpha ~ 1)),
start = list(fixed = coef(exp.5Delay)),
groups = ~id,
method = "ML",
verbose = 2,
control = list(msMaxIter = 50000,
niterEM = 5000,
maxIter = 5000,
pnlsTol = .01,
tolerance = .2,
apVar = T,
minScale = .0000001,
opt = "optim"), na.action = na.omit)
exp.5DelayCovMLM <- nlme(z ~ (10^(q0) * 10^((k+.5) *(exp(-10^(alpha)*10^(q0)*y)-1))),
data = subset(cleanLong, x == min(x)),
fixed = list(q0 ~ scale(FTNDnum),
alpha ~ scale(FTNDnum)),
random = list(pdSymm(q0 + alpha ~ 1)),
start = list(fixed = coef(exp.5DelayCovGNLS)),
groups = ~id,
method = "ML",
verbose = 2,
control = list(msMaxIter = 50000,
niterEM = 5000,
maxIter = 5000,
pnlsTol = .01,
tolerance = .01,
apVar = T,
minScale = .0000001,
opt = "optim"), na.action = na.omit)
summary(expDelayCovMLM)
round(summary(exp.5DelayCovMLM)$tTable, 3)
anova(rachlinDelayMLM, expDelayMLM, exp.5DelayMLM)
anova(rachlinDelayCovMLM, expDelayCovMLM, exp.5DelayCovMLM)
AICc(exp.5DemandCovMLM)
AICc(rachlinDemandCovMLM)
AICc(exp.5DelayCovMLM)
AICc(rachlinDelayCovMLM)
anova(rachlinDemandMLM, expDemandMLM, exp.5DemandMLM)
anova(rachlinDemandCovMLM, expDemandCovMLM, exp.5DemandCovMLM)
twoDcomparisons <- rbind(
anova(expDemandMLM, exp.5DemandMLM, rachlinDemandMLM),
anova(rachlinDelayMLM, expDelayMLM, exp.5DelayMLM)
)
rSquarerDemand <- function(beep){
1 - sum((predict(beep) - subset(cleanLong, y == min(y))$z)^2) / sum((mean(subset(cleanLong, y == min(y))$z) - subset(cleanLong, y == min(y))$z)^2)
}
RMSEDemand <- function(beep){
sqrt(mean((predict(beep) - subset(cleanLong, y == min(y))$z)^2))
}
MAEDemand <- function(beep){
mean(abs(predict(beep) - subset(cleanLong, y == min(y))$z))
}
rSquarerDelay <- function(beep){
1 - sum((predict(beep) - subset(cleanLong, x == min(x))$z)^2) / sum((mean(subset(cleanLong, x == min(x))$z) - subset(cleanLong, x == min(x))$z)^2)
}
RMSEDelay <- function(beep){
sqrt(mean((predict(beep) - subset(cleanLong, x == min(x))$z)^2))
}
MAEDelay <- function(beep){
mean(abs(predict(beep) - subset(cleanLong, x == min(x))$z))
}
r22D <- c(rSquarerDemand(expDemandMLM),
rSquarerDemand(exp.5DemandMLM),
rSquarerDemand(rachlinDemandMLM),
rSquarerDelay(rachlinDelayMLM),
rSquarerDelay(expDelayMLM),
rSquarerDelay(exp.5DelayMLM)
)
rmse2D <- c(RMSEDemand(expDemandMLM),
RMSEDemand(exp.5DemandMLM),
RMSEDemand(rachlinDemandMLM),
RMSEDelay(rachlinDelayMLM),
RMSEDelay(expDelayMLM),
RMSEDelay(exp.5DelayMLM)
)
mae2D <- c(MAEDemand(expDemandMLM),
MAEDemand(exp.5DemandMLM),
MAEDemand(rachlinDemandMLM),
MAEDelay(rachlinDelayMLM),
MAEDelay(expDelayMLM),
MAEDelay(exp.5DelayMLM)
)
AICc2D <- c(AICc(expDemandMLM),
AICc(exp.5DemandMLM),
AICc(rachlinDemandMLM),
AICc(rachlinDelayMLM),
AICc(expDelayMLM),
AICc(exp.5DelayMLM)
)
twoDcomparisons$call <- NULL
twoDcomparisons <- data.frame(twoDcomparisons)[,-c(6:8)]
data.frame(twoDcomparisons, RMSE = rmse2D, MAE = mae2D, R2 = r22D)
rbind(AICc(expDemandMLM), AICc(exp.5DemandMLM), AICc(rachlinDemandMLM))
rbind(AICc(expDelayMLM), AICc(exp.5DelayMLM), AICc(rachlinDelayMLM))
anova(expDemandCovMLM, rachlinDemandCovMLM)
anova(rachlinDelayCovMLM, expDelayCovMLM)
weightMaker <- function(x){
weights <- exp(-(1/2) * (x-min(x)))
probs <- exp(-(1/2) * (x-min(x))) / sum(exp(-(1/2) * (x-min(x))))
return(list(weights, probs))
}
weightMaker(c(AICc(exp.5DemandMLM), AICc(rachlinDemandMLM)))
weightMaker(c(AICc(rachlinDelayMLM), AICc(exp.5DelayMLM)))
weightMaker(c(BIC(exp.5DemandMLM), BIC(rachlinDemandMLM)))
weightMaker(c(BIC(rachlinDelayMLM), BIC(exp.5DelayMLM)))
# Equations used for analyses, ordered as presented in manuscript
koffExpDelDamMazurDenomForm <- z ~ (10^(q0) * 10^((k + .5) * (exp(-10^(alpha) * 10^(q0) * (x)) - 1))) / (1 + 10^b * y)
koffExpDelDamRachlinDenomForm <- z ~ (10^(q0) * 10^(k * (exp(-10^(alpha) * 10^(q0) * (x)) - 1))) / (1 + 10^b * y ^ s)
koff.5DelDamRachlinDenomForm <- z ~ (10^(q0) * 10^((k + .5) * (exp(-10^(alpha) * 10^(q0) * (x)) - 1))) / (1 + 10^b * y ^ s)
koffExpDelDamMGDenomForm <- z ~ (10^(q0) * 10^((k + .5) * (exp(-10^(alpha) * 10^(q0) * (x)) - 1))) / ((1 + 10^b * y )^ s)
koffMazurAddForm <- z ~ (10^(q0) * 10^((k + .5) * (exp(-10^(alpha) * 10^(q0) * (x)) - 1))) - (10^q0 * (1- (1/(1 + 10^b * y))))
koffMGAddForm <- z ~ (10^(q0) * 10^((k + .5) * (exp(-10^(alpha) * 10^(q0) * (x)) - 1))) - (10^q0 * (1- (1/(1 + 10^b * y) ^ s)))
koffRachlinAddForm <- z ~ (10^(q0) * 10^((k + .5) * (exp(-10^(alpha) * 10^(q0) * (x)) - 1))) - (10^q0 * (1- (1/(1 + 10^b * y ^ s))))
koffExpDelDamMazurDenomAlt <- z ~ (10^(q0) * 10^((k + .5) * (exp(-10^(alpha) * 10^(q0) * (y)) - 1))) / (1 + 10^b * x)
koffExpDelDamRachlinDenomAlt <- z ~ (10^(q0) * 10^((k + .5) * (exp(-10^(alpha) * 10^(q0) * (y)) - 1))) / (1 + 10^b * x ^ s)
koffExpDelDamMGDenomAlt <- z ~ (10^(q0) * 10^((k + .5) * (exp(-10^(alpha) * 10^(q0) * (y)) - 1))) / ((1 + 10^b * x )^ s)
koffMazurAddAlt <- z ~ (10^(q0) * 10^((k + .5) * (exp(-10^(alpha) * 10^(q0) * (y)) - 1))) - (10^q0 * (1- (1/(1 + 10^b * x))))
koffMGAddAlt <- z ~ (10^(q0) * 10^((k + .5) * (exp(-10^(alpha) * 10^(q0) * (y)) - 1))) - (10^q0 * (1- (1/(1 + 10^b * x) ^ s)))
koffRachlinAddAlt <- z ~ (10^(q0) * 10^((k + .5) * (exp(-10^(alpha) * 10^(q0) * (y)) - 1))) - (10^q0 * (1- (1/(1 + 10^b * x ^ s))))
delDamMazurForm <- z ~ (10^(q0)) / ((1 + 10^b * y) * (1 + 10^c * x))
delDamMGForm <- z ~ (10^(q0)) / (((1 + 10^b * y) ^ s) * ((1 + 10^c * x) ^ t))
delDamRachlinForm <- z ~ (10^(q0)) / ((1 + 10^b * y ^ s) * (1 + 10^c * x ^ t))
koffExpDelDamForm <- z ~ 10^(q0) * 10^(k * (exp(-10^(alpha) * 10^(q0) * (x)) - 1)) * 10^(k * (exp(-10^(beta) * 10^(q0) * (y)) - 1))
koffExpDelDam.5Form <- z ~ 10^(q0) * 10^((k + .5) * (exp(-10^(alpha) * 10^(q0) * (x)) - 1)) * 10^((k + .5) * (exp(-10^(beta) * 10^(q0) * (y)) - 1))
koffExpDelDamScalesForm <- z ~ 10^(q0) * 10^(k * (exp(-10^(alpha) * 10^(q0) * (x^t)) - 1)) * 10^(k * (exp(-10^(beta) * 10^(q0) * (y^s)) - 1))
koffExpDelDamScales.5Form <- z ~ 10^(q0) * 10^((k+.5) * (exp(-10^(alpha) * 10^(q0) * (x^t)) - 1)) * 10^((k + .5) * (exp(-10^(beta) * 10^(q0) * (y^s)) - 1))
# Determinining start values for MLMs ----
delDamKoffMazurAdd <- nls_multstart(koffMazurAddForm, data = cleanLong,
iter = 250,
start_lower = c(q0 = .1, alpha = -4, b = -4),
start_upper = c(q0 = 2, alpha = 4, b = 4))
delDamKoffMGAdd <- nls_multstart(koffMGAddForm, data = cleanLong,
iter = 250,
start_lower = c(q0 = .1, alpha = -4, b = -4, s = .1),
start_upper = c(q0 = 2, alpha = 4, b = 4, s = 4))
delDamKoffRachAdd <- nls_multstart(koffRachlinAddForm, data = cleanLong,
iter = 250,
start_lower = c(q0 = .1, alpha = -4, b = -4, s = .1),
start_upper = c(q0 = 2, alpha = 4, b = 4, s = 4))
delDamKoffMazurDenomLog <- nls_multstart(koffExpDelDamMazurDenomForm, data = cleanLong,
iter = 250,
start_lower = c(q0 = .1, alpha = -4, b = -4),
start_upper = c(q0 = 2, alpha = 4, b = 4))
delDamKoffRachlinDenomLog <- nls_multstart(koffExpDelDamRachlinDenomForm, data = cleanLong,
iter = 250,
start_lower = c(q0 = .1, alpha = -4, b = -4, s = .1),
start_upper = c(q0 = 2, alpha = 4, b = 4, s = 4))
delDamKoffMGDenomLog <- nls_multstart(koffExpDelDamMGDenomForm, data = cleanLong,
iter = 250,
start_lower = c(q0 = .1, alpha = -4, b = -4, s = .1),
start_upper = c(q0 = 2, alpha = 4, b = 4, s = 4))
delDamKoff.5RachlinDenomLog <- nls_multstart(koff.5DelDamRachlinDenomForm, data = cleanLong,
iter = 250,
start_lower = c(q0 = .1, alpha = -4, b = -4, s = .1),
start_upper = c(q0 = 2, alpha = 4, b = 4, s = 4))
altKoffMazurAdd <- nls_multstart(koffMazurAddAlt, data = cleanLong,
iter = 250,
start_lower = c(q0 = .1, alpha = -4, b = -4),
start_upper = c(q0 = 2, alpha = 4, b = 4))
altKoffMGAdd <- nls_multstart(koffMGAddAlt, data = cleanLong,
iter = 250,
start_lower = c(q0 = .1, alpha = -4, b = -4, s = .1),
start_upper = c(q0 = 2, alpha = 4, b = 4, s = 4))
altKoffRachAdd <- nls_multstart(koffRachlinAddAlt, data = cleanLong,
iter = 250,
start_lower = c(q0 = .1, alpha = -4, b = -4, s = .1),
start_upper = c(q0 = 2, alpha = 4, b = 4, s = 4))
altKoffMazurDenomLog <- nls_multstart(koffExpDelDamMazurDenomAlt, data = cleanLong,
iter = 250,
start_lower = c(q0 = .1, alpha = -4, b = -4),
start_upper = c(q0 = 2, alpha = 4, b = 4))
altKoffMGDenomLog <- nls_multstart(koffExpDelDamMGDenomAlt, data = cleanLong,
iter = 250,
start_lower = c(q0 = .1, alpha = -4, b = -4, s = .1),
start_upper = c(q0 = 2, alpha = 4, b = 4, s = 4))
altKoffRachlinDenomLog <- nls_multstart(koffExpDelDamRachlinDenomAlt, data = cleanLong,
iter = 250,
start_lower = c(q0 = .1, alpha = -4, b = -4, s = .1),
start_upper = c(q0 = 2, alpha = 4, b = 4, s = 4))
delDamMazurDenomLog <- nls_multstart(delDamMazurForm, data = cleanLong,
iter = 250,
start_lower = c(q0 = .1, b = -4, c = -4),
start_upper = c(q0 = 2, b = 4, c = 4))
delDamMGDenomLog <- nls_multstart(delDamMGForm, data = cleanLong,
iter = 250,
start_lower = c(q0 = .1, b = -4, s = .1, c = -4, t = .1),
start_upper = c(q0 = 2, b = 4, s = 4, c = 4, t = 4))
delDamRachlinDenomLog <- nls_multstart(delDamRachlinForm, data = cleanLong,
iter = 250,
start_lower = c(q0 = .1, b = -4, s = .1, c = -4, t = .1),
start_upper = c(q0 = 2, b = 4, s = 4, c = 4, t = 4))
delDamExpLog <- nls_multstart(koffExpDelDamForm, data = cleanLong,
iter = 250,
start_lower = c(q0 = .1, alpha = -4, beta = -4),
start_upper = c(q0 = 2, alpha = 4, beta = 4))
delDamExp.5Log <- nls_multstart(koffExpDelDam.5Form, data = cleanLong,
iter = 250,
start_lower = c(q0 = .1, alpha = -4, beta = -4),
start_upper = c(q0 = 2, alpha = 4, beta = 4))
delDamExpScalesLog <- nls_multstart(koffExpDelDamScalesForm, data = data.frame(cleanLong),
iter = 250,
start_lower = c(q0 = .1, alpha = -4, t = .1, beta = -4, s = .1),
start_upper = c(q0 = 2, alpha = 4, t = 4, beta = 4, s = 4))
delDamExpScales.5Log <- nls_multstart(koffExpDelDamScales.5Form, data = data.frame(cleanLong),
iter = 250,
start_lower = c(q0 = .1, alpha = -4, t = .1, beta = -4, s = .1),
start_upper = c(q0 = 2, alpha = 4, t = 4, beta = 4, s = 4))
# MLM comparisons----
nlmeMazurAddLog <- nlme(koffMazurAddForm,
data = cleanLong,
fixed = list(q0 ~ 1,
alpha ~ 1,
b ~ 1),
random = list(pdSymm(q0 + alpha + b~ 1)),
start = list(fixed = coef(delDamKoffMazurAdd)),
groups = ~id,
method = "ML",
verbose = 2,
control = list(msMaxIter = 50000,
niterEM = 5000,
maxIter = 5000,
pnlsTol = .0001,
tolerance = .3,
apVar = T,
minScale = .0000001,
opt = "optim"))
nlmeMGAddLog <- nlme(koffMGAddForm,
data = cleanLong,
fixed = list(q0 ~ 1,
alpha ~ 1,
b ~ 1,
s ~ 1),
random = list(pdSymm(q0 + alpha + b + s ~ 1)),
start = list(fixed = coef(delDamKoffMGAdd)),
groups = ~id,
method = "ML",
verbose = 2,
control = list(msMaxIter = 50000,
niterEM = 5000,
maxIter = 5000,
pnlsTol = .0001,
tolerance = .3,
apVar = T,
minScale = .0000001,
opt = "optim"))
nlmeRachAddLog <- nlme(koffRachlinAddForm,
data = cleanLong,
fixed = list(q0 ~ 1,
alpha ~ 1,
b ~ 1,
s ~ 1),
random = list(pdSymm(q0 + alpha + b + s ~ 1)),
start = list(fixed = coef(delDamKoffRachAdd)),
groups = ~id,
method = "ML",
verbose = 2,
control = list(msMaxIter = 50000,
niterEM = 5000,
maxIter = 5000,
pnlsTol = .0001,
tolerance = .3,
apVar = T,
minScale = .0000001,
opt = "optim"))
nlmeMixedMazurLog <- nlme(koffExpDelDamMazurDenomForm,
data = cleanLong,
fixed = list(q0 ~ 1,
alpha ~ 1,
b ~ 1),
random = list(pdSymm(q0 + alpha + b ~ 1)),
start = list(fixed = coef(delDamKoffMazurDenomLog)),
groups = ~id,
method = "ML",
verbose = 2,
control = list(msMaxIter = 50000,
niterEM = 5000,
maxIter = 5000,
pnlsTol = .0001,
tolerance = .2,
apVar = T,
minScale = .0000001,
opt = "optim"))
nlmeMixedRachlinLog <- nlme(koffExpDelDamRachlinDenomForm,
data = cleanLong,
fixed = list(q0 ~ 1,
alpha ~ 1,
b ~ 1,
s ~ 1),
random = list(pdSymm(q0 + alpha + b + s ~ 1)),
start = list(fixed = coef(delDamKoffRachlinDenomLog)),
groups = ~id,
method = "ML",
verbose = 2,
control = list(msMaxIter = 50000,
niterEM = 5000,
maxIter = 5000,
pnlsTol = .0001,
tolerance = .3,
apVar = T,
minScale = .0000001,
opt = "optim"))
nlmeMixedMGLog <- nlme(koffExpDelDamMGDenomForm,
data = cleanLong,
fixed = list(q0 ~ 1,
alpha ~ 1,
b ~ 1,
s ~ 1),
random = list(pdSymm(q0 + alpha + b + s ~ 1)),
start = list(fixed = coef(delDamKoffMGDenomLog)),
groups = ~id,
method = "ML",
verbose = 2,
control = list(msMaxIter = 50000,
niterEM = 5000,
maxIter = 5000,
pnlsTol = .0001,
tolerance = .5,
apVar = T,
minScale = .0000001,
opt = "optim"))
nlmeMixed.5RachlinLog <- nlme(koff.5DelDamRachlinDenomForm,
data = cleanLong,
fixed = list(q0 ~ 1,
alpha ~ 1,
b ~ 1,
s ~ 1),
random = list(pdSymm(q0 + alpha + b + s ~ 1)),
start = list(fixed = coef(delDamKoff.5RachlinDenomLog)),
groups = ~id,
method = "ML",
verbose = 2,
control = list(msMaxIter = 50000,
niterEM = 5000,
maxIter = 5000,
pnlsTol = .0001,
tolerance = .4,
apVar = T,
minScale = .0000001,
opt = "optim"))
nlmeMazurAddLogAlt <- nlme(koffMazurAddAlt,
data = cleanLong,
fixed = list(q0 ~ 1,
alpha ~ 1,
b ~ 1),
random = list(pdSymm(q0 + alpha + b~ 1)),
start = list(fixed = coef(altKoffMazurAdd)),
groups = ~id,
method = "ML",
verbose = 2,
control = list(msMaxIter = 50000,
niterEM = 5000,
maxIter = 5000,
pnlsTol = .0001,
tolerance = .2,
apVar = T,
minScale = .0000001,
opt = "optim"))
nlmeMGAddLogAlt <- nlme(koffMGAddAlt,
data = cleanLong,
fixed = list(q0 ~ 1,
alpha ~ 1,
b ~ 1,
s ~ 1),
random = list(pdSymm(q0 + alpha + b + s ~ 1)),
start = list(fixed = coef(altKoffMGAdd)),
groups = ~id,
method = "ML",
verbose = 2,
control = list(msMaxIter = 50000,
niterEM = 5000,
maxIter = 5000,
pnlsTol = .0001,
tolerance = .3,
apVar = T,
minScale = .0000001,
opt = "optim"))
nlmeRachAddLogAlt <- nlme(koffRachlinAddAlt,
data = cleanLong,
fixed = list(q0 ~ 1,
alpha ~ 1,
b ~ 1,
s ~ 1),
random = list(pdSymm(q0 + alpha + b + s ~ 1)),
start = list(fixed = coef(altKoffRachAdd)),
groups = ~id,
method = "ML",
verbose = 2,
control = list(msMaxIter = 50000,
niterEM = 5000,
maxIter = 5000,
pnlsTol = .0001,
tolerance = .2,
apVar = T,
minScale = .0000001,
opt = "optim"))
nlmeMixedMazurLogAlt <- nlme(koffExpDelDamMazurDenomAlt,
data = cleanLong,
fixed = list(q0 ~ 1,
alpha ~ 1,
b ~ 1),
random = list(pdSymm(q0 + alpha + b ~ 1)),
start = list(fixed = coef(altKoffMazurDenomLog)),
groups = ~id,
method = "ML",
verbose = 2,
control = list(msMaxIter = 50000,
niterEM = 5000,
maxIter = 5000,
pnlsTol = .0001,
tolerance = .2,
apVar = T,
minScale = .0000001,
opt = "optim"))
nlmeMixedMGLogAlt <- nlme(koffExpDelDamMGDenomAlt,
data = cleanLong,
fixed = list(q0 ~ 1,
alpha ~ 1,
b ~ 1,
s ~ 1),
random = list(pdSymm(q0 + alpha + b + s ~ 1)),
start = list(fixed = coef(altKoffMGDenomLog)),
groups = ~id,
method = "ML",
verbose = 2,
control = list(msMaxIter = 50000,
niterEM = 5000,
maxIter = 5000,
pnlsTol = .0001,
tolerance = .5,
apVar = T,
minScale = .0000001,
opt = "optim"))
nlmeMixedRachlinLogAlt <- nlme(koffExpDelDamRachlinDenomAlt,
data = cleanLong,
fixed = list(q0 ~ 1,
alpha ~ 1,
b ~ 1,
s ~ 1),
random = list(pdSymm(q0 + alpha + b + s ~ 1)),
start = list(fixed = coef(altKoffRachlinDenomLog)),
groups = ~id,
method = "ML",
verbose = 2,
control = list(msMaxIter = 50000,
niterEM = 5000,
maxIter = 5000,
pnlsTol = .0001,
tolerance = .4,
apVar = T,
minScale = .0000001,
opt = "optim"))