############################################################
## Multinomial logit data analysis example : Travel types ##
############################################################
# People in the US make travel choices among ‘short domestic’, ‘long domestic’ and ‘international’
# Outcome variables: short domestic vs. long domestic vs. international
# Predictors: social economic status (categorical) and sensitivity to new environment (continuous; inversely coded)
# The number of observation is 200
# Response variables: Program choice
# international is the reference category, j = 0
# short domestic is the j = 1 category
# long domestic is the j = 2 category
# Explanatory variables
# sensitivity to new environment: continuous variable X1
# Social economic status (ses): categorical variable
# ses low
# ses middle
# ses high
# gender: categorical variable
# gender female
# gender male
# Load packages
require(foreign)
## Loading required package: foreign
require(nnet)
## Loading required package: nnet
require(ggplot2)
## Loading required package: ggplot2
require(reshape2)
## Loading required package: reshape2
# Read data
travel <- read.csv(file = "C:/Users/ehk994/Desktop/Teaching/Fall 2021/IMC465_Marketing Model II/Week 3 - Advanced choice data model/travel.csv", sep=",")
str(travel)
## 'data.frame': 200 obs. of 4 variables:
## $ gender : chr "male" "female" "female" "female" ...
## $ ses : chr "low" "middle" "high" "low" ...
## $ travel : chr "longDom" "shortDom" "longDom" "longDom" ...
## $ sensitivity: int 35 33 39 37 31 36 36 31 41 37 ...
travel$gender <- as.factor(travel$gender)
travel$ses <- as.factor(travel$ses)
travel$travel <- as.factor(travel$travel)
## Description of Data
with(travel, table(ses, travel))
## travel
## ses international longDom shortDom
## high 42 7 9
## low 19 12 16
## middle 44 31 20
with(travel, do.call(rbind, tapply(sensitivity, travel, function(x) c(M = mean(x), SD = sd(x)))))
## M SD
## international 56.25714 7.943343
## longDom 46.76000 9.318754
## shortDom 51.33333 9.397775
## Set reference level
travel$travel <- relevel(travel$travel, ref = "international")
travel$ses <- relevel(travel$ses, ref = "low")
travel$gender <- relevel(travel$gender, ref = "male")
## Run multinomial model
travelml <- multinom(travel ~ ses + gender + sensitivity, data = travel)
## # weights: 18 (10 variable)
## initial value 219.722458
## iter 10 value 179.062277
## final value 178.858982
## converged
summary(travelml)
## Call:
## multinom(formula = travel ~ ses + gender + sensitivity, data = travel)
##
## Coefficients:
## (Intercept) seshigh sesmiddle genderfemale sensitivity
## longDom 5.949238 -0.8192132 0.4068942 -0.60630493 -0.12456991
## shortDom 2.933717 -1.1472828 -0.5189852 -0.07993732 -0.05896894
##
## Std. Errors:
## (Intercept) seshigh sesmiddle genderfemale sensitivity
## longDom 1.291404 0.6070211 0.4863972 0.4225750 0.02390876
## shortDom 1.257426 0.5229032 0.4506561 0.3967909 0.02236772
##
## Residual Deviance: 357.718
## AIC: 377.718
## Odds (relative risks)
# Exponentiate the coefficients to get risk ratios
exp(coef(travelml))
## (Intercept) seshigh sesmiddle genderfemale sensitivity
## longDom 383.46115 0.4407783 1.5021452 0.5453623 0.8828765
## shortDom 18.79737 0.3174983 0.5951242 0.9231742 0.9427361
## z test statistics to find p-values
z <- summary(travelml)$coefficients/summary(travelml)$standard.errors
z
## (Intercept) seshigh sesmiddle genderfemale sensitivity
## longDom 4.606800 -1.349563 0.8365472 -1.4347865 -5.210220
## shortDom 2.333114 -2.194063 -1.1516214 -0.2014595 -2.636341
## 2-tailed z test: p-values
p <- 2*pnorm(-abs(z))
p
## (Intercept) seshigh sesmiddle genderfemale sensitivity
## longDom 4.089138e-06 0.17715618 0.4028472 0.1513479 1.886167e-07
## shortDom 1.964219e-02 0.02823085 0.2494767 0.8403393 8.380543e-03
## Predicted probabilities for each of the outcome levels (each obs)
head(pp <- fitted(travelml))
## international longDom shortDom
## 1 0.1206750 0.5913409 0.2879841
## 2 0.1311413 0.6753940 0.1934647
## 3 0.4408788 0.3155332 0.2435880
## 4 0.1983698 0.4132199 0.3884103
## 5 0.1079086 0.7129739 0.1791175
## 6 0.2761470 0.5266003 0.1972527
## Fitted probabilities
# 'sensitivity' at its mean
mean(travel$sensitivity)
## [1] 52.775
## Probability varying the levels or values of each variable
dwrite <- data.frame(ses = rep(c("low", "middle", "high"), each = 82), gender = rep(c("male", "female"), each = 41), sensitivity = rep(c(30:70),
3))
# store the predicted probabilities for each value of ses and write
pp.write <- cbind(dwrite, predict(travelml, newdata = dwrite, type = "probs", se = TRUE))
lpp <- melt(pp.write, id.vars = c("ses", "gender", "sensitivity"), value.name = "probability")
head(lpp) # view first few rows
## ses gender sensitivity variable probability
## 1 low male 30 international 0.07496222
## 2 low male 31 international 0.08273639
## 3 low male 32 international 0.09116656
## 4 low male 33 international 0.10028246
## 5 low male 34 international 0.11011088
## 6 low male 35 international 0.12067501
## Calculate the mean probabilities within each level of ses
by(pp.write[, 4:6], pp.write$ses, colMeans)
## pp.write$ses: high
## international longDom shortDom
## 0.6050407 0.2206906 0.1742688
## ------------------------------------------------------------
## pp.write$ses: low
## international longDom shortDom
## 0.4056048 0.2666280 0.3277672
## ------------------------------------------------------------
## pp.write$ses: middle
## international longDom shortDom
## 0.4248199 0.3788666 0.1963135
## Likelihood ratio test 1
# with 'gender' vs without 'gender'
# model
mod2 <- multinom(travel ~ ses + gender + sensitivity, data = travel)
## # weights: 18 (10 variable)
## initial value 219.722458
## iter 10 value 179.062277
## final value 178.858982
## converged
logLik(mod2)
## 'log Lik.' -178.859 (df=10)
# Nested model
mod <- multinom(travel ~ ses + sensitivity, data = travel)
## # weights: 15 (8 variable)
## initial value 219.722458
## iter 10 value 179.982880
## final value 179.981726
## converged
logLik(mod)
## 'log Lik.' -179.9817 (df=8)
# Degree of freedom
df <- length(coef(mod2)) - length(coef(mod))
df
## [1] 2
# Test statistics and p-value
teststat<--2*(as.numeric(logLik(mod))-as.numeric(logLik(mod2)))
teststat
## [1] 2.245489
pchisq(teststat,df=2,lower.tail=FALSE)
## [1] 0.3253855
## Likelihood ratio test 2
# with sensitivity vs without sensitivity
# model
mod2 <- multinom(travel ~ ses + gender + sensitivity, data = travel)
## # weights: 18 (10 variable)
## initial value 219.722458
## iter 10 value 179.062277
## final value 178.858982
## converged
logLik(mod2)
## 'log Lik.' -178.859 (df=10)
# Nested model
mod <- multinom(travel ~ ses + gender, data = travel)
## # weights: 15 (8 variable)
## initial value 219.722458
## iter 10 value 195.534775
## final value 195.520828
## converged
logLik(mod)
## 'log Lik.' -195.5208 (df=8)
# Degree of freedom
df <- length(coef(mod2)) - length(coef(mod))
df
## [1] 2
# Test statistics and p-value
teststat<--2*(as.numeric(logLik(mod))-as.numeric(logLik(mod2)))
teststat
## [1] 33.32369
pchisq(teststat,df=2,lower.tail=FALSE)
## [1] 5.805666e-08
#vReject H0: keep ses in the model
############################################################
## Ordered logit data analysis example 1: Wine repurchase ##
############################################################
# Number of obs: 400
# Response variable Y: “How likely will you purchase a certain wine?”
# high probability
# medium probability, and
# low probability
# Predictors:
# coupon: yes (1), no (0)
# peers: yes (1), no (0)
# quality: quality rating by experts from zero to five
## Load packages
require(foreign)
require(ggplot2)
require(MASS)
## Loading required package: MASS
require(Hmisc)
## Loading required package: Hmisc
## Loading required package: lattice
## Loading required package: survival
## Warning: package 'survival' was built under R version 4.1.1
## Loading required package: Formula
##
## Attaching package: 'Hmisc'
## The following objects are masked from 'package:base':
##
## format.pval, units
require(reshape2)
## Read data
coupon <- read.csv(file='C:/Users/ehk994/Desktop/Teaching/Marketing Model II/4 - Ordered and conditional logistic/Ordered logit/class_example_coupon_data.csv', stringsAsFactors = F, header=T, na.strings=c("","NA"))
## Look at the first few lines
head(coupon)
## Number rpurchase coupon peers quality
## 1 1 high probability 0 0 3.25
## 2 2 medium probability 1 0 3.20
## 3 3 low probability 1 1 3.93
## 4 4 medium probability 0 0 2.80
## 5 5 medium probability 0 0 2.52
## 6 6 low probability 0 1 2.58
## Range, mean and sd of quality
range(coupon$quality)
## [1] 1.89 3.99
summary(coupon$quality)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1.890 2.710 2.980 2.989 3.260 3.990
sd(coupon$quality)
## [1] 0.3979409
## Frequencies
# one at a time, table rpurchase, coupon and peers
lapply(coupon[, c("rpurchase", "coupon", "peers")], table)
## $rpurchase
##
## high probability low probability medium probability
## 40 220 140
##
## $coupon
##
## 0 1
## 337 63
##
## $peers
##
## 0 1
## 343 57
# Three way cross tabs
ftable(xtabs(~ rpurchase + coupon + peers, data = coupon))
## peers 0 1
## rpurchase coupon
## high probability 0 20 7
## 1 10 3
## low probability 0 175 25
## 1 14 6
## medium probability 0 98 12
## 1 26 4
# Boxplot
ggplot(coupon, aes(x = rpurchase, y = quality)) +
geom_boxplot(size = .75) +
geom_jitter(alpha = .5) +
facet_grid(coupon ~ peers, margins = TRUE) +
theme(axis.text.x = element_text(angle = 45, hjust = 1, vjust = 1))
## Fit ordered logit model and store results 'm'
# Recode the y variables
library(dplyr)
##
## Attaching package: 'dplyr'
## The following objects are masked from 'package:Hmisc':
##
## src, summarize
## The following object is masked from 'package:MASS':
##
## select
## The following objects are masked from 'package:stats':
##
## filter, lag
## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union
coupon$rpurchase2<-recode(coupon$rpurchase, "low probability" = 1, "medium probability" = 2, "high probability" = 3)
coupon$rpurchase2 <- as.factor(coupon$rpurchase2)
m <- polr(rpurchase2 ~ coupon + peers + quality, data = coupon, Hess=TRUE)
# We specify Hess=TRUE to have the model return the observed information matrix from optimization (called the Hessian) which is used to get standard errors.
## View a summary of the model
summary(m)
## Call:
## polr(formula = rpurchase2 ~ coupon + peers + quality, data = coupon,
## Hess = TRUE)
##
## Coefficients:
## Value Std. Error t value
## coupon 1.04770 0.2658 3.9419
## peers -0.05881 0.2979 -0.1975
## quality 0.61597 0.2606 2.3633
##
## Intercepts:
## Value Std. Error t value
## 1|2 2.1978 0.7770 2.8287
## 2|3 4.2933 0.8018 5.3546
##
## Residual Deviance: 717.0249
## AIC: 727.0249
## p-values
(ctable <- coef(summary(m)))
## Value Std. Error t value
## coupon 1.04770355 0.2657895 3.9418551
## peers -0.05881433 0.2978621 -0.1974549
## quality 0.61596621 0.2606343 2.3633348
## 1|2 2.19783331 0.7769700 2.8287234
## 2|3 4.29328052 0.8017936 5.3545958
## calculate and store p values
p <- pnorm(abs(ctable[, "t value"]), lower.tail = FALSE) * 2
p
## coupon peers quality 1|2 2|3
## 8.085382e-05 8.434716e-01 1.811130e-02 4.673406e-03 8.574790e-08
## combined table
(ctable <- cbind(ctable, "p value" = p))
## Value Std. Error t value p value
## coupon 1.04770355 0.2657895 3.9418551 8.085382e-05
## peers -0.05881433 0.2978621 -0.1974549 8.434716e-01
## quality 0.61596621 0.2606343 2.3633348 1.811130e-02
## 1|2 2.19783331 0.7769700 2.8287234 4.673406e-03
## 2|3 4.29328052 0.8017936 5.3545958 8.574790e-08
(ci <- confint(m)) # default method gives profiled CIs
## Waiting for profiling to be done...
## 2.5 % 97.5 %
## coupon 0.5281767 1.5721750
## peers -0.6522060 0.5191385
## quality 0.1076201 1.1309148
## OR and CI
exp(cbind(OR = coef(m), ci))
## OR 2.5 % 97.5 %
## coupon 2.8510962 1.6958375 4.817114
## peers 0.9428818 0.5208954 1.680579
## quality 1.8514446 1.1136246 3.098490
## Predicted probabilities
newdat <- data.frame(
coupon = rep(0:1, 200),
peers = rep(0:1, each = 200),
quality = rep(seq(from = 1.9, to = 4, length.out = 100), 4))
## Look at the first few lines
head(newdat)
## coupon peers quality
## 1 0 0 1.900000
## 2 1 0 1.921212
## 3 0 0 1.942424
## 4 1 0 1.963636
## 5 0 0 1.984848
## 6 1 0 2.006061
## Combine with probabilities
newdat <- cbind(newdat, predict(m, newdat, type = "probs"))
##show first few rows
head(newdat)
## coupon peers quality 1 2 3
## 1 0 0 1.900000 0.7364304 0.2213989 0.04217067
## 2 1 0 1.921212 0.4916828 0.3954893 0.11282791
## 3 0 0 1.942424 0.7313270 0.2254341 0.04323891
## 4 1 0 1.963636 0.4851534 0.3993764 0.11547024
## 5 0 0 1.984848 0.7261615 0.2295056 0.04433297
## 6 1 0 2.006061 0.4786291 0.4032047 0.11816621
## reshape for plots
library(reshape2)
lnewdat <- melt(newdat, id.vars = c("coupon", "peers", "quality"),
variable.name = "Level", value.name="Probability")
## view first few rows
head(lnewdat)
## coupon peers quality Level Probability
## 1 0 0 1.900000 1 0.7364304
## 2 1 0 1.921212 1 0.4916828
## 3 0 0 1.942424 1 0.7313270
## 4 1 0 1.963636 1 0.4851534
## 5 0 0 1.984848 1 0.7261615
## 6 1 0 2.006061 1 0.4786291
## Plot
ggplot(lnewdat, aes(x = quality, y = Probability, colour = Level)) +
geom_line() + facet_grid(coupon ~ peers, labeller="label_both")
# plot in left upper side: Other variables fixed at: No coupon and no peer recommendation
###########################################################
##### Ordered logit data analysis example 2: Opinion ######
###########################################################
# Number of obs: 70
# Response variable Y (opinion):
# strongly disagree
# disagree
# agree
# strongly agree
# Predictors (continuous):
# x1
# x2
# x3
## Getting sample data
library(foreign)
orderData <- read.dta("https://dss.princeton.edu/training/Panel101.dta")
orderData <- orderData[c(5:8)]
## Summary of variables
summary(orderData)
## x1 x2 x3 opinion
## Min. :-0.5676 Min. :-1.6218 Min. :-1.16539 Str agree:20
## 1st Qu.: 0.3290 1st Qu.:-1.2156 1st Qu.:-0.07931 Agree :15
## Median : 0.6413 Median :-0.4621 Median : 0.51419 Disag :19
## Mean : 0.6480 Mean : 0.1339 Mean : 0.76185 Str disag:16
## 3rd Qu.: 1.0958 3rd Qu.: 1.6078 3rd Qu.: 1.15486
## Max. : 1.4464 Max. : 2.5303 Max. : 7.16892
## Look at the first few lines
head(orderData)
## x1 x2 x3 opinion
## 1 0.2779036 -1.1079559 0.28255358 Str agree
## 2 0.3206847 -0.9487200 0.49253848 Disag
## 3 0.3634657 -0.7894840 0.70252335 Disag
## 4 0.2461440 -0.8855330 -0.09439092 Disag
## 5 0.4246230 -0.7297683 0.94613063 Disag
## 6 0.4772141 -0.7232460 1.02968037 Str agree
## Model
m1 <- polr(opinion ~ x1 + x2 + x3, data=orderData, Hess=TRUE)
summary(m1)
## Call:
## polr(formula = opinion ~ x1 + x2 + x3, data = orderData, Hess = TRUE)
##
## Coefficients:
## Value Std. Error t value
## x1 0.98140 0.5641 1.7397
## x2 0.24936 0.2086 1.1954
## x3 0.09089 0.1549 0.5867
##
## Intercepts:
## Value Std. Error t value
## Str agree|Agree -0.2054 0.4682 -0.4388
## Agree|Disag 0.7370 0.4697 1.5690
## Disag|Str disag 1.9951 0.5204 3.8335
##
## Residual Deviance: 189.6382
## AIC: 201.6382
## Odds ratio (risk ratios)
m1.or=exp(coef(m1))
m1.or
## x1 x2 x3
## 2.668179 1.283198 1.095150
## Predicted probabilities
m1.pred <- predict(m1, type="probs")
summary(m1.pred)
## Str agree Agree Disag Str disag
## Min. :0.1040 Min. :0.1255 Min. :0.1458 Min. :0.07418
## 1st Qu.:0.2307 1st Qu.:0.2038 1st Qu.:0.2511 1st Qu.:0.17350
## Median :0.2628 Median :0.2144 Median :0.2851 Median :0.23705
## Mean :0.2869 Mean :0.2124 Mean :0.2715 Mean :0.22923
## 3rd Qu.:0.3458 3rd Qu.:0.2271 3rd Qu.:0.2949 3rd Qu.:0.26968
## Max. :0.5802 Max. :0.2313 Max. :0.3045 Max. :0.48832
# Predicted probabilities
newdat <- data.frame(
x1 = rep(seq(from = -0.5676, to = 1.4464, length.out = 100), 4),
x2 = rep(seq(from = -1.6218, to = 2.5303, length.out = 100), 4),
x3 = rep(seq(from = -1.1654, to = 7.1689, length.out = 100), 4))
newdat <- cbind(newdat, predict(m1, newdat, type = "probs"))
##show first few rows
head(newdat)
## x1 x2 x3 Str agree Agree Disag Str disag
## 1 -0.5676000 -1.621800 -1.1654000 0.7030665 0.1556096 0.09664083 0.04468304
## 2 -0.5472566 -1.579860 -1.0812152 0.6950569 0.1589354 0.09967090 0.04633679
## 3 -0.5269131 -1.537919 -0.9970303 0.6869275 0.1622530 0.10277082 0.04804866
## 4 -0.5065697 -1.495979 -0.9128455 0.6786815 0.1655575 0.10594045 0.04982048
## 5 -0.4862263 -1.454038 -0.8286606 0.6703226 0.1688438 0.10917953 0.05165408
## 6 -0.4658828 -1.412098 -0.7444758 0.6618546 0.1721064 0.11248764 0.05355137
# Reshape the data long with the reshape2 package and plot all of the predicted probabilities for the different conditions
lnewdat <- melt(newdat, id.vars = c("x1", "x2", "x3"),
variable.name = "Level", value.name="Probability")
# view first few rows
head(lnewdat)
## x1 x2 x3 Level Probability
## 1 -0.5676000 -1.621800 -1.1654000 Str agree 0.7030665
## 2 -0.5472566 -1.579860 -1.0812152 Str agree 0.6950569
## 3 -0.5269131 -1.537919 -0.9970303 Str agree 0.6869275
## 4 -0.5065697 -1.495979 -0.9128455 Str agree 0.6786815
## 5 -0.4862263 -1.454038 -0.8286606 Str agree 0.6703226
## 6 -0.4658828 -1.412098 -0.7444758 Str agree 0.6618546
# Use class for the predicted category
newdat[, c("pred.prob")] <- predict(m1, newdata=newdat, type="class")
newdat
## x1 x2 x3 Str agree Agree Disag
## 1 -0.567600000 -1.62180000 -1.16540000 0.70306653 0.15560960 0.09664083
## 2 -0.547256566 -1.57985960 -1.08121515 0.69505694 0.15893537 0.09967090
## 3 -0.526913131 -1.53791919 -0.99703030 0.68692750 0.16225302 0.10277082
## 4 -0.506569697 -1.49597879 -0.91284545 0.67868153 0.16555755 0.10594045
## 5 -0.486226263 -1.45403838 -0.82866061 0.67032260 0.16884379 0.10917953
## 6 -0.465882828 -1.41209798 -0.74447576 0.66185456 0.17210643 0.11248764
## 7 -0.445539394 -1.37015758 -0.66029091 0.65328152 0.17534002 0.11586420
## 8 -0.425195960 -1.32821717 -0.57610606 0.64460784 0.17853895 0.11930849
## 9 -0.404852525 -1.28627677 -0.49192121 0.63583813 0.18169753 0.12281957
## 10 -0.384509091 -1.24433636 -0.40773636 0.62697724 0.18480996 0.12639637
## 11 -0.364165657 -1.20239596 -0.32355152 0.61803027 0.18787037 0.13003759
## 12 -0.343822222 -1.16045556 -0.23936667 0.60900253 0.19087282 0.13374175
## 13 -0.323478788 -1.11851515 -0.15518182 0.59989955 0.19381136 0.13750715
## 14 -0.303135354 -1.07657475 -0.07099697 0.59072707 0.19667998 0.14133188
## 15 -0.282791919 -1.03463434 0.01318788 0.58149101 0.19947271 0.14521381
## 16 -0.262448485 -0.99269394 0.09737273 0.57219746 0.20218360 0.14915059
## 17 -0.242105051 -0.95075354 0.18155758 0.56285268 0.20480674 0.15313962
## 18 -0.221761616 -0.90881313 0.26574242 0.55346307 0.20733631 0.15717806
## 19 -0.201418182 -0.86687273 0.34992727 0.54403516 0.20976660 0.16126285
## 20 -0.181074747 -0.82493232 0.43411212 0.53457559 0.21209201 0.16539065
## 21 -0.160731313 -0.78299192 0.51829697 0.52509108 0.21430709 0.16955788
## 22 -0.140387879 -0.74105152 0.60248182 0.51558844 0.21640658 0.17376071
## 23 -0.120044444 -0.69911111 0.68666667 0.50607451 0.21838542 0.17799505
## 24 -0.099701010 -0.65717071 0.77085152 0.49655618 0.22023878 0.18225657
## 25 -0.079357576 -0.61523030 0.85503636 0.48704034 0.22196207 0.18654065
## 26 -0.059014141 -0.57328990 0.93922121 0.47753389 0.22355096 0.19084246
## 27 -0.038670707 -0.53134949 1.02340606 0.46804369 0.22500146 0.19515690
## 28 -0.018327273 -0.48940909 1.10759091 0.45857655 0.22630984 0.19947861
## 29 0.002016162 -0.44746869 1.19177576 0.44913922 0.22747274 0.20380203
## 30 0.022359596 -0.40552828 1.27596061 0.43973837 0.22848715 0.20812136
## 31 0.042703030 -0.36358788 1.36014545 0.43038056 0.22935040 0.21243055
## 32 0.063046465 -0.32164747 1.44433030 0.42107221 0.23006024 0.21672339
## 33 0.083389899 -0.27970707 1.52851515 0.41181964 0.23061480 0.22099344
## 34 0.103733333 -0.23776667 1.61270000 0.40262899 0.23101259 0.22523408
## 35 0.124076768 -0.19582626 1.69688485 0.39350622 0.23125257 0.22943854
## 36 0.144420202 -0.15388586 1.78106970 0.38445712 0.23133409 0.23359989
## 37 0.164763636 -0.11194545 1.86525455 0.37548729 0.23125694 0.23771107
## 38 0.185107071 -0.07000505 1.94943939 0.36660209 0.23102132 0.24176490
## 39 0.205450505 -0.02806465 2.03362424 0.35780668 0.23062787 0.24575414
## 40 0.225793939 0.01387576 2.11780909 0.34910598 0.23007762 0.24967144
## 41 0.246137374 0.05581616 2.20199394 0.34050468 0.22937203 0.25350945
## 42 0.266480808 0.09775657 2.28617879 0.33200720 0.22851298 0.25726076
## 43 0.286824242 0.13969697 2.37036364 0.32361772 0.22750270 0.26091801
## 44 0.307167677 0.18163737 2.45454848 0.31534015 0.22634386 0.26447384
## 45 0.327511111 0.22357778 2.53873333 0.30717816 0.22503944 0.26792097
## 46 0.347854545 0.26551818 2.62291818 0.29913513 0.22359282 0.27125221
## 47 0.368197980 0.30745859 2.70710303 0.29121417 0.22200768 0.27446047
## 48 0.388541414 0.34939899 2.79128788 0.28341814 0.22028805 0.27753883
## 49 0.408884848 0.39133939 2.87547273 0.27574961 0.21843821 0.28048053
## 50 0.429228283 0.43327980 2.95965758 0.26821092 0.21646277 0.28327903
## 51 0.449571717 0.47522020 3.04384242 0.26080411 0.21436653 0.28592801
## 52 0.469915152 0.51716061 3.12802727 0.25353097 0.21215456 0.28842141
## 53 0.490258586 0.55910101 3.21221212 0.24639306 0.20983213 0.29075347
## 54 0.510602020 0.60104141 3.29639697 0.23939166 0.20740466 0.29291873
## 55 0.530945455 0.64298182 3.38058182 0.23252782 0.20487774 0.29491208
## 56 0.551288889 0.68492222 3.46476667 0.22580236 0.20225710 0.29672875
## 57 0.571632323 0.72686263 3.54895152 0.21921586 0.19954856 0.29836439
## 58 0.591975758 0.76880303 3.63313636 0.21276868 0.19675800 0.29981503
## 59 0.612319192 0.81074343 3.71732121 0.20646098 0.19389139 0.30107714
## 60 0.632662626 0.85268384 3.80150606 0.20029270 0.19095471 0.30214762
## 61 0.653006061 0.89462424 3.88569091 0.19426358 0.18795393 0.30302382
## 62 0.673349495 0.93656465 3.96987576 0.18837321 0.18489504 0.30370359
## 63 0.693692929 0.97850505 4.05406061 0.18262095 0.18178396 0.30418524
## 64 0.714036364 1.02044545 4.13824545 0.17700605 0.17862658 0.30446756
## 65 0.734379798 1.06238586 4.22243030 0.17152755 0.17542868 0.30454985
## 66 0.754723232 1.10432626 4.30661515 0.16618438 0.17219598 0.30443191
## 67 0.775066667 1.14626667 4.39080000 0.16097531 0.16893406 0.30411404
## 68 0.795410101 1.18820707 4.47498485 0.15589899 0.16564840 0.30359701
## 69 0.815753535 1.23014747 4.55916970 0.15095394 0.16234430 0.30288213
## 70 0.836096970 1.27208788 4.64335455 0.14613860 0.15902695 0.30197116
## 71 0.856440404 1.31402828 4.72753939 0.14145128 0.15570133 0.30086635
## 72 0.876783838 1.35596869 4.81172424 0.13689019 0.15237229 0.29957043
## 73 0.897127273 1.39790909 4.89590909 0.13245349 0.14904446 0.29808658
## 74 0.917470707 1.43984949 4.98009394 0.12813923 0.14572229 0.29641840
## 75 0.937814141 1.48178990 5.06427879 0.12394542 0.14241004 0.29456994
## 76 0.958157576 1.52373030 5.14846364 0.11987000 0.13911176 0.29254562
## 77 0.978501010 1.56567071 5.23264848 0.11591085 0.13583129 0.29035028
## 78 0.998844444 1.60761111 5.31683333 0.11206582 0.13257226 0.28798909
## 79 1.019187879 1.64955152 5.40101818 0.10833270 0.12933812 0.28546755
## 80 1.039531313 1.69149192 5.48520303 0.10470928 0.12613207 0.28279150
## 81 1.059874747 1.73343232 5.56938788 0.10119330 0.12295713 0.27996703
## 82 1.080218182 1.77537273 5.65357273 0.09778248 0.11981608 0.27700051
## 83 1.100561616 1.81731313 5.73775758 0.09447455 0.11671154 0.27389852
## 84 1.120905051 1.85925354 5.82194242 0.09126720 0.11364589 0.27066785
## 85 1.141248485 1.90119394 5.90612727 0.08815813 0.11062133 0.26731546
## 86 1.161591919 1.94313434 5.99031212 0.08514506 0.10763986 0.26384844
## 87 1.181935354 1.98507475 6.07449697 0.08222568 0.10470330 0.26027402
## 88 1.202278788 2.02701515 6.15868182 0.07939771 0.10181327 0.25659948
## 89 1.222622222 2.06895556 6.24286667 0.07665887 0.09897123 0.25283219
## 90 1.242965657 2.11089596 6.32705152 0.07400692 0.09617847 0.24897952
## 91 1.263309091 2.15283636 6.41123636 0.07143962 0.09343609 0.24504887
## 92 1.283652525 2.19477677 6.49542121 0.06895474 0.09074506 0.24104760
## 93 1.303995960 2.23671717 6.57960606 0.06655010 0.08810619 0.23698302
## 94 1.324339394 2.27865758 6.66379091 0.06422353 0.08552015 0.23286239
## 95 1.344682828 2.32059798 6.74797576 0.06197289 0.08298745 0.22869285
## 96 1.365026263 2.36253838 6.83216061 0.05979609 0.08050851 0.22448144
## 97 1.385369697 2.40447879 6.91634545 0.05769104 0.07808360 0.22023507
## 98 1.405713131 2.44641919 7.00053030 0.05565572 0.07571288 0.21596049
## 99 1.426056566 2.48835960 7.08471515 0.05368811 0.07339639 0.21166428
## 100 1.446400000 2.53030000 7.16890000 0.05178624 0.07113410 0.20735283
## 101 -0.567600000 -1.62180000 -1.16540000 0.70306653 0.15560960 0.09664083
## 102 -0.547256566 -1.57985960 -1.08121515 0.69505694 0.15893537 0.09967090
## 103 -0.526913131 -1.53791919 -0.99703030 0.68692750 0.16225302 0.10277082
## 104 -0.506569697 -1.49597879 -0.91284545 0.67868153 0.16555755 0.10594045
## 105 -0.486226263 -1.45403838 -0.82866061 0.67032260 0.16884379 0.10917953
## 106 -0.465882828 -1.41209798 -0.74447576 0.66185456 0.17210643 0.11248764
## 107 -0.445539394 -1.37015758 -0.66029091 0.65328152 0.17534002 0.11586420
## 108 -0.425195960 -1.32821717 -0.57610606 0.64460784 0.17853895 0.11930849
## 109 -0.404852525 -1.28627677 -0.49192121 0.63583813 0.18169753 0.12281957
## 110 -0.384509091 -1.24433636 -0.40773636 0.62697724 0.18480996 0.12639637
## 111 -0.364165657 -1.20239596 -0.32355152 0.61803027 0.18787037 0.13003759
## 112 -0.343822222 -1.16045556 -0.23936667 0.60900253 0.19087282 0.13374175
## 113 -0.323478788 -1.11851515 -0.15518182 0.59989955 0.19381136 0.13750715
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## 115 -0.282791919 -1.03463434 0.01318788 0.58149101 0.19947271 0.14521381
## 116 -0.262448485 -0.99269394 0.09737273 0.57219746 0.20218360 0.14915059
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## 118 -0.221761616 -0.90881313 0.26574242 0.55346307 0.20733631 0.15717806
## 119 -0.201418182 -0.86687273 0.34992727 0.54403516 0.20976660 0.16126285
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## 121 -0.160731313 -0.78299192 0.51829697 0.52509108 0.21430709 0.16955788
## 122 -0.140387879 -0.74105152 0.60248182 0.51558844 0.21640658 0.17376071
## 123 -0.120044444 -0.69911111 0.68666667 0.50607451 0.21838542 0.17799505
## 124 -0.099701010 -0.65717071 0.77085152 0.49655618 0.22023878 0.18225657
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## 126 -0.059014141 -0.57328990 0.93922121 0.47753389 0.22355096 0.19084246
## 127 -0.038670707 -0.53134949 1.02340606 0.46804369 0.22500146 0.19515690
## 128 -0.018327273 -0.48940909 1.10759091 0.45857655 0.22630984 0.19947861
## 129 0.002016162 -0.44746869 1.19177576 0.44913922 0.22747274 0.20380203
## 130 0.022359596 -0.40552828 1.27596061 0.43973837 0.22848715 0.20812136
## 131 0.042703030 -0.36358788 1.36014545 0.43038056 0.22935040 0.21243055
## 132 0.063046465 -0.32164747 1.44433030 0.42107221 0.23006024 0.21672339
## 133 0.083389899 -0.27970707 1.52851515 0.41181964 0.23061480 0.22099344
## 134 0.103733333 -0.23776667 1.61270000 0.40262899 0.23101259 0.22523408
## 135 0.124076768 -0.19582626 1.69688485 0.39350622 0.23125257 0.22943854
## 136 0.144420202 -0.15388586 1.78106970 0.38445712 0.23133409 0.23359989
## 137 0.164763636 -0.11194545 1.86525455 0.37548729 0.23125694 0.23771107
## 138 0.185107071 -0.07000505 1.94943939 0.36660209 0.23102132 0.24176490
## 139 0.205450505 -0.02806465 2.03362424 0.35780668 0.23062787 0.24575414
## 140 0.225793939 0.01387576 2.11780909 0.34910598 0.23007762 0.24967144
## 141 0.246137374 0.05581616 2.20199394 0.34050468 0.22937203 0.25350945
## 142 0.266480808 0.09775657 2.28617879 0.33200720 0.22851298 0.25726076
## 143 0.286824242 0.13969697 2.37036364 0.32361772 0.22750270 0.26091801
## 144 0.307167677 0.18163737 2.45454848 0.31534015 0.22634386 0.26447384
## 145 0.327511111 0.22357778 2.53873333 0.30717816 0.22503944 0.26792097
## 146 0.347854545 0.26551818 2.62291818 0.29913513 0.22359282 0.27125221
## 147 0.368197980 0.30745859 2.70710303 0.29121417 0.22200768 0.27446047
## 148 0.388541414 0.34939899 2.79128788 0.28341814 0.22028805 0.27753883
## 149 0.408884848 0.39133939 2.87547273 0.27574961 0.21843821 0.28048053
## 150 0.429228283 0.43327980 2.95965758 0.26821092 0.21646277 0.28327903
## 151 0.449571717 0.47522020 3.04384242 0.26080411 0.21436653 0.28592801
## 152 0.469915152 0.51716061 3.12802727 0.25353097 0.21215456 0.28842141
## 153 0.490258586 0.55910101 3.21221212 0.24639306 0.20983213 0.29075347
## 154 0.510602020 0.60104141 3.29639697 0.23939166 0.20740466 0.29291873
## 155 0.530945455 0.64298182 3.38058182 0.23252782 0.20487774 0.29491208
## 156 0.551288889 0.68492222 3.46476667 0.22580236 0.20225710 0.29672875
## 157 0.571632323 0.72686263 3.54895152 0.21921586 0.19954856 0.29836439
## 158 0.591975758 0.76880303 3.63313636 0.21276868 0.19675800 0.29981503
## 159 0.612319192 0.81074343 3.71732121 0.20646098 0.19389139 0.30107714
## 160 0.632662626 0.85268384 3.80150606 0.20029270 0.19095471 0.30214762
## 161 0.653006061 0.89462424 3.88569091 0.19426358 0.18795393 0.30302382
## 162 0.673349495 0.93656465 3.96987576 0.18837321 0.18489504 0.30370359
## 163 0.693692929 0.97850505 4.05406061 0.18262095 0.18178396 0.30418524
## 164 0.714036364 1.02044545 4.13824545 0.17700605 0.17862658 0.30446756
## 165 0.734379798 1.06238586 4.22243030 0.17152755 0.17542868 0.30454985
## 166 0.754723232 1.10432626 4.30661515 0.16618438 0.17219598 0.30443191
## 167 0.775066667 1.14626667 4.39080000 0.16097531 0.16893406 0.30411404
## 168 0.795410101 1.18820707 4.47498485 0.15589899 0.16564840 0.30359701
## 169 0.815753535 1.23014747 4.55916970 0.15095394 0.16234430 0.30288213
## 170 0.836096970 1.27208788 4.64335455 0.14613860 0.15902695 0.30197116
## 171 0.856440404 1.31402828 4.72753939 0.14145128 0.15570133 0.30086635
## 172 0.876783838 1.35596869 4.81172424 0.13689019 0.15237229 0.29957043
## 173 0.897127273 1.39790909 4.89590909 0.13245349 0.14904446 0.29808658
## 174 0.917470707 1.43984949 4.98009394 0.12813923 0.14572229 0.29641840
## 175 0.937814141 1.48178990 5.06427879 0.12394542 0.14241004 0.29456994
## 176 0.958157576 1.52373030 5.14846364 0.11987000 0.13911176 0.29254562
## 177 0.978501010 1.56567071 5.23264848 0.11591085 0.13583129 0.29035028
## 178 0.998844444 1.60761111 5.31683333 0.11206582 0.13257226 0.28798909
## 179 1.019187879 1.64955152 5.40101818 0.10833270 0.12933812 0.28546755
## 180 1.039531313 1.69149192 5.48520303 0.10470928 0.12613207 0.28279150
## 181 1.059874747 1.73343232 5.56938788 0.10119330 0.12295713 0.27996703
## 182 1.080218182 1.77537273 5.65357273 0.09778248 0.11981608 0.27700051
## 183 1.100561616 1.81731313 5.73775758 0.09447455 0.11671154 0.27389852
## 184 1.120905051 1.85925354 5.82194242 0.09126720 0.11364589 0.27066785
## 185 1.141248485 1.90119394 5.90612727 0.08815813 0.11062133 0.26731546
## 186 1.161591919 1.94313434 5.99031212 0.08514506 0.10763986 0.26384844
## 187 1.181935354 1.98507475 6.07449697 0.08222568 0.10470330 0.26027402
## 188 1.202278788 2.02701515 6.15868182 0.07939771 0.10181327 0.25659948
## 189 1.222622222 2.06895556 6.24286667 0.07665887 0.09897123 0.25283219
## 190 1.242965657 2.11089596 6.32705152 0.07400692 0.09617847 0.24897952
## 191 1.263309091 2.15283636 6.41123636 0.07143962 0.09343609 0.24504887
## 192 1.283652525 2.19477677 6.49542121 0.06895474 0.09074506 0.24104760
## 193 1.303995960 2.23671717 6.57960606 0.06655010 0.08810619 0.23698302
## 194 1.324339394 2.27865758 6.66379091 0.06422353 0.08552015 0.23286239
## 195 1.344682828 2.32059798 6.74797576 0.06197289 0.08298745 0.22869285
## 196 1.365026263 2.36253838 6.83216061 0.05979609 0.08050851 0.22448144
## 197 1.385369697 2.40447879 6.91634545 0.05769104 0.07808360 0.22023507
## 198 1.405713131 2.44641919 7.00053030 0.05565572 0.07571288 0.21596049
## 199 1.426056566 2.48835960 7.08471515 0.05368811 0.07339639 0.21166428
## 200 1.446400000 2.53030000 7.16890000 0.05178624 0.07113410 0.20735283
## 201 -0.567600000 -1.62180000 -1.16540000 0.70306653 0.15560960 0.09664083
## 202 -0.547256566 -1.57985960 -1.08121515 0.69505694 0.15893537 0.09967090
## 203 -0.526913131 -1.53791919 -0.99703030 0.68692750 0.16225302 0.10277082
## 204 -0.506569697 -1.49597879 -0.91284545 0.67868153 0.16555755 0.10594045
## 205 -0.486226263 -1.45403838 -0.82866061 0.67032260 0.16884379 0.10917953
## 206 -0.465882828 -1.41209798 -0.74447576 0.66185456 0.17210643 0.11248764
## 207 -0.445539394 -1.37015758 -0.66029091 0.65328152 0.17534002 0.11586420
## 208 -0.425195960 -1.32821717 -0.57610606 0.64460784 0.17853895 0.11930849
## 209 -0.404852525 -1.28627677 -0.49192121 0.63583813 0.18169753 0.12281957
## 210 -0.384509091 -1.24433636 -0.40773636 0.62697724 0.18480996 0.12639637
## 211 -0.364165657 -1.20239596 -0.32355152 0.61803027 0.18787037 0.13003759
## 212 -0.343822222 -1.16045556 -0.23936667 0.60900253 0.19087282 0.13374175
## 213 -0.323478788 -1.11851515 -0.15518182 0.59989955 0.19381136 0.13750715
## 214 -0.303135354 -1.07657475 -0.07099697 0.59072707 0.19667998 0.14133188
## 215 -0.282791919 -1.03463434 0.01318788 0.58149101 0.19947271 0.14521381
## 216 -0.262448485 -0.99269394 0.09737273 0.57219746 0.20218360 0.14915059
## 217 -0.242105051 -0.95075354 0.18155758 0.56285268 0.20480674 0.15313962
## 218 -0.221761616 -0.90881313 0.26574242 0.55346307 0.20733631 0.15717806
## 219 -0.201418182 -0.86687273 0.34992727 0.54403516 0.20976660 0.16126285
## 220 -0.181074747 -0.82493232 0.43411212 0.53457559 0.21209201 0.16539065
## 221 -0.160731313 -0.78299192 0.51829697 0.52509108 0.21430709 0.16955788
## 222 -0.140387879 -0.74105152 0.60248182 0.51558844 0.21640658 0.17376071
## 223 -0.120044444 -0.69911111 0.68666667 0.50607451 0.21838542 0.17799505
## 224 -0.099701010 -0.65717071 0.77085152 0.49655618 0.22023878 0.18225657
## 225 -0.079357576 -0.61523030 0.85503636 0.48704034 0.22196207 0.18654065
## 226 -0.059014141 -0.57328990 0.93922121 0.47753389 0.22355096 0.19084246
## 227 -0.038670707 -0.53134949 1.02340606 0.46804369 0.22500146 0.19515690
## 228 -0.018327273 -0.48940909 1.10759091 0.45857655 0.22630984 0.19947861
## 229 0.002016162 -0.44746869 1.19177576 0.44913922 0.22747274 0.20380203
## 230 0.022359596 -0.40552828 1.27596061 0.43973837 0.22848715 0.20812136
## 231 0.042703030 -0.36358788 1.36014545 0.43038056 0.22935040 0.21243055
## 232 0.063046465 -0.32164747 1.44433030 0.42107221 0.23006024 0.21672339
## 233 0.083389899 -0.27970707 1.52851515 0.41181964 0.23061480 0.22099344
## 234 0.103733333 -0.23776667 1.61270000 0.40262899 0.23101259 0.22523408
## 235 0.124076768 -0.19582626 1.69688485 0.39350622 0.23125257 0.22943854
## 236 0.144420202 -0.15388586 1.78106970 0.38445712 0.23133409 0.23359989
## 237 0.164763636 -0.11194545 1.86525455 0.37548729 0.23125694 0.23771107
## 238 0.185107071 -0.07000505 1.94943939 0.36660209 0.23102132 0.24176490
## 239 0.205450505 -0.02806465 2.03362424 0.35780668 0.23062787 0.24575414
## 240 0.225793939 0.01387576 2.11780909 0.34910598 0.23007762 0.24967144
## 241 0.246137374 0.05581616 2.20199394 0.34050468 0.22937203 0.25350945
## 242 0.266480808 0.09775657 2.28617879 0.33200720 0.22851298 0.25726076
## 243 0.286824242 0.13969697 2.37036364 0.32361772 0.22750270 0.26091801
## 244 0.307167677 0.18163737 2.45454848 0.31534015 0.22634386 0.26447384
## 245 0.327511111 0.22357778 2.53873333 0.30717816 0.22503944 0.26792097
## 246 0.347854545 0.26551818 2.62291818 0.29913513 0.22359282 0.27125221
## 247 0.368197980 0.30745859 2.70710303 0.29121417 0.22200768 0.27446047
## 248 0.388541414 0.34939899 2.79128788 0.28341814 0.22028805 0.27753883
## 249 0.408884848 0.39133939 2.87547273 0.27574961 0.21843821 0.28048053
## 250 0.429228283 0.43327980 2.95965758 0.26821092 0.21646277 0.28327903
## 251 0.449571717 0.47522020 3.04384242 0.26080411 0.21436653 0.28592801
## 252 0.469915152 0.51716061 3.12802727 0.25353097 0.21215456 0.28842141
## 253 0.490258586 0.55910101 3.21221212 0.24639306 0.20983213 0.29075347
## 254 0.510602020 0.60104141 3.29639697 0.23939166 0.20740466 0.29291873
## 255 0.530945455 0.64298182 3.38058182 0.23252782 0.20487774 0.29491208
## 256 0.551288889 0.68492222 3.46476667 0.22580236 0.20225710 0.29672875
## 257 0.571632323 0.72686263 3.54895152 0.21921586 0.19954856 0.29836439
## 258 0.591975758 0.76880303 3.63313636 0.21276868 0.19675800 0.29981503
## 259 0.612319192 0.81074343 3.71732121 0.20646098 0.19389139 0.30107714
## 260 0.632662626 0.85268384 3.80150606 0.20029270 0.19095471 0.30214762
## 261 0.653006061 0.89462424 3.88569091 0.19426358 0.18795393 0.30302382
## 262 0.673349495 0.93656465 3.96987576 0.18837321 0.18489504 0.30370359
## 263 0.693692929 0.97850505 4.05406061 0.18262095 0.18178396 0.30418524
## 264 0.714036364 1.02044545 4.13824545 0.17700605 0.17862658 0.30446756
## 265 0.734379798 1.06238586 4.22243030 0.17152755 0.17542868 0.30454985
## 266 0.754723232 1.10432626 4.30661515 0.16618438 0.17219598 0.30443191
## 267 0.775066667 1.14626667 4.39080000 0.16097531 0.16893406 0.30411404
## 268 0.795410101 1.18820707 4.47498485 0.15589899 0.16564840 0.30359701
## 269 0.815753535 1.23014747 4.55916970 0.15095394 0.16234430 0.30288213
## 270 0.836096970 1.27208788 4.64335455 0.14613860 0.15902695 0.30197116
## 271 0.856440404 1.31402828 4.72753939 0.14145128 0.15570133 0.30086635
## 272 0.876783838 1.35596869 4.81172424 0.13689019 0.15237229 0.29957043
## 273 0.897127273 1.39790909 4.89590909 0.13245349 0.14904446 0.29808658
## 274 0.917470707 1.43984949 4.98009394 0.12813923 0.14572229 0.29641840
## 275 0.937814141 1.48178990 5.06427879 0.12394542 0.14241004 0.29456994
## 276 0.958157576 1.52373030 5.14846364 0.11987000 0.13911176 0.29254562
## 277 0.978501010 1.56567071 5.23264848 0.11591085 0.13583129 0.29035028
## 278 0.998844444 1.60761111 5.31683333 0.11206582 0.13257226 0.28798909
## 279 1.019187879 1.64955152 5.40101818 0.10833270 0.12933812 0.28546755
## 280 1.039531313 1.69149192 5.48520303 0.10470928 0.12613207 0.28279150
## 281 1.059874747 1.73343232 5.56938788 0.10119330 0.12295713 0.27996703
## 282 1.080218182 1.77537273 5.65357273 0.09778248 0.11981608 0.27700051
## 283 1.100561616 1.81731313 5.73775758 0.09447455 0.11671154 0.27389852
## 284 1.120905051 1.85925354 5.82194242 0.09126720 0.11364589 0.27066785
## 285 1.141248485 1.90119394 5.90612727 0.08815813 0.11062133 0.26731546
## 286 1.161591919 1.94313434 5.99031212 0.08514506 0.10763986 0.26384844
## 287 1.181935354 1.98507475 6.07449697 0.08222568 0.10470330 0.26027402
## 288 1.202278788 2.02701515 6.15868182 0.07939771 0.10181327 0.25659948
## 289 1.222622222 2.06895556 6.24286667 0.07665887 0.09897123 0.25283219
## 290 1.242965657 2.11089596 6.32705152 0.07400692 0.09617847 0.24897952
## 291 1.263309091 2.15283636 6.41123636 0.07143962 0.09343609 0.24504887
## 292 1.283652525 2.19477677 6.49542121 0.06895474 0.09074506 0.24104760
## 293 1.303995960 2.23671717 6.57960606 0.06655010 0.08810619 0.23698302
## 294 1.324339394 2.27865758 6.66379091 0.06422353 0.08552015 0.23286239
## 295 1.344682828 2.32059798 6.74797576 0.06197289 0.08298745 0.22869285
## 296 1.365026263 2.36253838 6.83216061 0.05979609 0.08050851 0.22448144
## 297 1.385369697 2.40447879 6.91634545 0.05769104 0.07808360 0.22023507
## 298 1.405713131 2.44641919 7.00053030 0.05565572 0.07571288 0.21596049
## 299 1.426056566 2.48835960 7.08471515 0.05368811 0.07339639 0.21166428
## 300 1.446400000 2.53030000 7.16890000 0.05178624 0.07113410 0.20735283
## 301 -0.567600000 -1.62180000 -1.16540000 0.70306653 0.15560960 0.09664083
## 302 -0.547256566 -1.57985960 -1.08121515 0.69505694 0.15893537 0.09967090
## 303 -0.526913131 -1.53791919 -0.99703030 0.68692750 0.16225302 0.10277082
## 304 -0.506569697 -1.49597879 -0.91284545 0.67868153 0.16555755 0.10594045
## 305 -0.486226263 -1.45403838 -0.82866061 0.67032260 0.16884379 0.10917953
## 306 -0.465882828 -1.41209798 -0.74447576 0.66185456 0.17210643 0.11248764
## 307 -0.445539394 -1.37015758 -0.66029091 0.65328152 0.17534002 0.11586420
## 308 -0.425195960 -1.32821717 -0.57610606 0.64460784 0.17853895 0.11930849
## 309 -0.404852525 -1.28627677 -0.49192121 0.63583813 0.18169753 0.12281957
## 310 -0.384509091 -1.24433636 -0.40773636 0.62697724 0.18480996 0.12639637
## 311 -0.364165657 -1.20239596 -0.32355152 0.61803027 0.18787037 0.13003759
## 312 -0.343822222 -1.16045556 -0.23936667 0.60900253 0.19087282 0.13374175
## 313 -0.323478788 -1.11851515 -0.15518182 0.59989955 0.19381136 0.13750715
## 314 -0.303135354 -1.07657475 -0.07099697 0.59072707 0.19667998 0.14133188
## 315 -0.282791919 -1.03463434 0.01318788 0.58149101 0.19947271 0.14521381
## 316 -0.262448485 -0.99269394 0.09737273 0.57219746 0.20218360 0.14915059
## 317 -0.242105051 -0.95075354 0.18155758 0.56285268 0.20480674 0.15313962
## 318 -0.221761616 -0.90881313 0.26574242 0.55346307 0.20733631 0.15717806
## 319 -0.201418182 -0.86687273 0.34992727 0.54403516 0.20976660 0.16126285
## 320 -0.181074747 -0.82493232 0.43411212 0.53457559 0.21209201 0.16539065
## 321 -0.160731313 -0.78299192 0.51829697 0.52509108 0.21430709 0.16955788
## 322 -0.140387879 -0.74105152 0.60248182 0.51558844 0.21640658 0.17376071
## 323 -0.120044444 -0.69911111 0.68666667 0.50607451 0.21838542 0.17799505
## 324 -0.099701010 -0.65717071 0.77085152 0.49655618 0.22023878 0.18225657
## 325 -0.079357576 -0.61523030 0.85503636 0.48704034 0.22196207 0.18654065
## 326 -0.059014141 -0.57328990 0.93922121 0.47753389 0.22355096 0.19084246
## 327 -0.038670707 -0.53134949 1.02340606 0.46804369 0.22500146 0.19515690
## 328 -0.018327273 -0.48940909 1.10759091 0.45857655 0.22630984 0.19947861
## 329 0.002016162 -0.44746869 1.19177576 0.44913922 0.22747274 0.20380203
## 330 0.022359596 -0.40552828 1.27596061 0.43973837 0.22848715 0.20812136
## 331 0.042703030 -0.36358788 1.36014545 0.43038056 0.22935040 0.21243055
## 332 0.063046465 -0.32164747 1.44433030 0.42107221 0.23006024 0.21672339
## 333 0.083389899 -0.27970707 1.52851515 0.41181964 0.23061480 0.22099344
## 334 0.103733333 -0.23776667 1.61270000 0.40262899 0.23101259 0.22523408
## 335 0.124076768 -0.19582626 1.69688485 0.39350622 0.23125257 0.22943854
## 336 0.144420202 -0.15388586 1.78106970 0.38445712 0.23133409 0.23359989
## 337 0.164763636 -0.11194545 1.86525455 0.37548729 0.23125694 0.23771107
## 338 0.185107071 -0.07000505 1.94943939 0.36660209 0.23102132 0.24176490
## 339 0.205450505 -0.02806465 2.03362424 0.35780668 0.23062787 0.24575414
## 340 0.225793939 0.01387576 2.11780909 0.34910598 0.23007762 0.24967144
## 341 0.246137374 0.05581616 2.20199394 0.34050468 0.22937203 0.25350945
## 342 0.266480808 0.09775657 2.28617879 0.33200720 0.22851298 0.25726076
## 343 0.286824242 0.13969697 2.37036364 0.32361772 0.22750270 0.26091801
## 344 0.307167677 0.18163737 2.45454848 0.31534015 0.22634386 0.26447384
## 345 0.327511111 0.22357778 2.53873333 0.30717816 0.22503944 0.26792097
## 346 0.347854545 0.26551818 2.62291818 0.29913513 0.22359282 0.27125221
## 347 0.368197980 0.30745859 2.70710303 0.29121417 0.22200768 0.27446047
## 348 0.388541414 0.34939899 2.79128788 0.28341814 0.22028805 0.27753883
## 349 0.408884848 0.39133939 2.87547273 0.27574961 0.21843821 0.28048053
## 350 0.429228283 0.43327980 2.95965758 0.26821092 0.21646277 0.28327903
## 351 0.449571717 0.47522020 3.04384242 0.26080411 0.21436653 0.28592801
## 352 0.469915152 0.51716061 3.12802727 0.25353097 0.21215456 0.28842141
## 353 0.490258586 0.55910101 3.21221212 0.24639306 0.20983213 0.29075347
## 354 0.510602020 0.60104141 3.29639697 0.23939166 0.20740466 0.29291873
## 355 0.530945455 0.64298182 3.38058182 0.23252782 0.20487774 0.29491208
## 356 0.551288889 0.68492222 3.46476667 0.22580236 0.20225710 0.29672875
## 357 0.571632323 0.72686263 3.54895152 0.21921586 0.19954856 0.29836439
## 358 0.591975758 0.76880303 3.63313636 0.21276868 0.19675800 0.29981503
## 359 0.612319192 0.81074343 3.71732121 0.20646098 0.19389139 0.30107714
## 360 0.632662626 0.85268384 3.80150606 0.20029270 0.19095471 0.30214762
## 361 0.653006061 0.89462424 3.88569091 0.19426358 0.18795393 0.30302382
## 362 0.673349495 0.93656465 3.96987576 0.18837321 0.18489504 0.30370359
## 363 0.693692929 0.97850505 4.05406061 0.18262095 0.18178396 0.30418524
## 364 0.714036364 1.02044545 4.13824545 0.17700605 0.17862658 0.30446756
## 365 0.734379798 1.06238586 4.22243030 0.17152755 0.17542868 0.30454985
## 366 0.754723232 1.10432626 4.30661515 0.16618438 0.17219598 0.30443191
## 367 0.775066667 1.14626667 4.39080000 0.16097531 0.16893406 0.30411404
## 368 0.795410101 1.18820707 4.47498485 0.15589899 0.16564840 0.30359701
## 369 0.815753535 1.23014747 4.55916970 0.15095394 0.16234430 0.30288213
## 370 0.836096970 1.27208788 4.64335455 0.14613860 0.15902695 0.30197116
## 371 0.856440404 1.31402828 4.72753939 0.14145128 0.15570133 0.30086635
## 372 0.876783838 1.35596869 4.81172424 0.13689019 0.15237229 0.29957043
## 373 0.897127273 1.39790909 4.89590909 0.13245349 0.14904446 0.29808658
## 374 0.917470707 1.43984949 4.98009394 0.12813923 0.14572229 0.29641840
## 375 0.937814141 1.48178990 5.06427879 0.12394542 0.14241004 0.29456994
## 376 0.958157576 1.52373030 5.14846364 0.11987000 0.13911176 0.29254562
## 377 0.978501010 1.56567071 5.23264848 0.11591085 0.13583129 0.29035028
## 378 0.998844444 1.60761111 5.31683333 0.11206582 0.13257226 0.28798909
## 379 1.019187879 1.64955152 5.40101818 0.10833270 0.12933812 0.28546755
## 380 1.039531313 1.69149192 5.48520303 0.10470928 0.12613207 0.28279150
## 381 1.059874747 1.73343232 5.56938788 0.10119330 0.12295713 0.27996703
## 382 1.080218182 1.77537273 5.65357273 0.09778248 0.11981608 0.27700051
## 383 1.100561616 1.81731313 5.73775758 0.09447455 0.11671154 0.27389852
## 384 1.120905051 1.85925354 5.82194242 0.09126720 0.11364589 0.27066785
## 385 1.141248485 1.90119394 5.90612727 0.08815813 0.11062133 0.26731546
## 386 1.161591919 1.94313434 5.99031212 0.08514506 0.10763986 0.26384844
## 387 1.181935354 1.98507475 6.07449697 0.08222568 0.10470330 0.26027402
## 388 1.202278788 2.02701515 6.15868182 0.07939771 0.10181327 0.25659948
## 389 1.222622222 2.06895556 6.24286667 0.07665887 0.09897123 0.25283219
## 390 1.242965657 2.11089596 6.32705152 0.07400692 0.09617847 0.24897952
## 391 1.263309091 2.15283636 6.41123636 0.07143962 0.09343609 0.24504887
## 392 1.283652525 2.19477677 6.49542121 0.06895474 0.09074506 0.24104760
## 393 1.303995960 2.23671717 6.57960606 0.06655010 0.08810619 0.23698302
## 394 1.324339394 2.27865758 6.66379091 0.06422353 0.08552015 0.23286239
## 395 1.344682828 2.32059798 6.74797576 0.06197289 0.08298745 0.22869285
## 396 1.365026263 2.36253838 6.83216061 0.05979609 0.08050851 0.22448144
## 397 1.385369697 2.40447879 6.91634545 0.05769104 0.07808360 0.22023507
## 398 1.405713131 2.44641919 7.00053030 0.05565572 0.07571288 0.21596049
## 399 1.426056566 2.48835960 7.08471515 0.05368811 0.07339639 0.21166428
## 400 1.446400000 2.53030000 7.16890000 0.05178624 0.07113410 0.20735283
## Str disag pred.prob
## 1 0.04468304 Str agree
## 2 0.04633679 Str agree
## 3 0.04804866 Str agree
## 4 0.04982048 Str agree
## 5 0.05165408 Str agree
## 6 0.05355137 Str agree
## 7 0.05551426 Str agree
## 8 0.05754473 Str agree
## 9 0.05964477 Str agree
## 10 0.06181643 Str agree
## 11 0.06406177 Str agree
## 12 0.06638289 Str agree
## 13 0.06878194 Str agree
## 14 0.07126107 Str agree
## 15 0.07382247 Str agree
## 16 0.07646836 Str agree
## 17 0.07920097 Str agree
## 18 0.08202255 Str agree
## 19 0.08493539 Str agree
## 20 0.08794176 Str agree
## 21 0.09104395 Str agree
## 22 0.09424427 Str agree
## 23 0.09754501 Str agree
## 24 0.10094847 Str agree
## 25 0.10445694 Str agree
## 26 0.10807268 Str agree
## 27 0.11179796 Str agree
## 28 0.11563500 Str agree
## 29 0.11958600 Str agree
## 30 0.12365312 Str agree
## 31 0.12783849 Str agree
## 32 0.13214415 Str agree
## 33 0.13657212 Str agree
## 34 0.14112434 Str agree
## 35 0.14580268 Str agree
## 36 0.15060890 Str agree
## 37 0.15554471 Str agree
## 38 0.16061169 Str agree
## 39 0.16581132 Str agree
## 40 0.17114496 Str agree
## 41 0.17661384 Str agree
## 42 0.18221906 Str agree
## 43 0.18796157 Str agree
## 44 0.19384215 Str agree
## 45 0.19986142 Str agree
## 46 0.20601985 Str agree
## 47 0.21231768 Str agree
## 48 0.21875499 Str agree
## 49 0.22533164 Disag
## 50 0.23204728 Disag
## 51 0.23890135 Disag
## 52 0.24589305 Disag
## 53 0.25302134 Disag
## 54 0.26028495 Disag
## 55 0.26768236 Disag
## 56 0.27521178 Disag
## 57 0.28287119 Disag
## 58 0.29065828 Disag
## 59 0.29857049 Disag
## 60 0.30660498 Str disag
## 61 0.31475866 Str disag
## 62 0.32302816 Str disag
## 63 0.33140985 Str disag
## 64 0.33989982 Str disag
## 65 0.34849392 Str disag
## 66 0.35718773 Str disag
## 67 0.36597660 Str disag
## 68 0.37485561 Str disag
## 69 0.38381963 Str disag
## 70 0.39286330 Str disag
## 71 0.40198104 Str disag
## 72 0.41116709 Str disag
## 73 0.42041547 Str disag
## 74 0.42972007 Str disag
## 75 0.43907460 Str disag
## 76 0.44847262 Str disag
## 77 0.45790758 Str disag
## 78 0.46737283 Str disag
## 79 0.47686163 Str disag
## 80 0.48636715 Str disag
## 81 0.49588255 Str disag
## 82 0.50540093 Str disag
## 83 0.51491540 Str disag
## 84 0.52441907 Str disag
## 85 0.53390508 Str disag
## 86 0.54336664 Str disag
## 87 0.55279701 Str disag
## 88 0.56218954 Str disag
## 89 0.57153771 Str disag
## 90 0.58083509 Str disag
## 91 0.59007543 Str disag
## 92 0.59925260 Str disag
## 93 0.60836069 Str disag
## 94 0.61739394 Str disag
## 95 0.62634680 Str disag
## 96 0.63521395 Str disag
## 97 0.64399028 Str disag
## 98 0.65267092 Str disag
## 99 0.66125123 Str disag
## 100 0.66972683 Str disag
## 101 0.04468304 Str agree
## 102 0.04633679 Str agree
## 103 0.04804866 Str agree
## 104 0.04982048 Str agree
## 105 0.05165408 Str agree
## 106 0.05355137 Str agree
## 107 0.05551426 Str agree
## 108 0.05754473 Str agree
## 109 0.05964477 Str agree
## 110 0.06181643 Str agree
## 111 0.06406177 Str agree
## 112 0.06638289 Str agree
## 113 0.06878194 Str agree
## 114 0.07126107 Str agree
## 115 0.07382247 Str agree
## 116 0.07646836 Str agree
## 117 0.07920097 Str agree
## 118 0.08202255 Str agree
## 119 0.08493539 Str agree
## 120 0.08794176 Str agree
## 121 0.09104395 Str agree
## 122 0.09424427 Str agree
## 123 0.09754501 Str agree
## 124 0.10094847 Str agree
## 125 0.10445694 Str agree
## 126 0.10807268 Str agree
## 127 0.11179796 Str agree
## 128 0.11563500 Str agree
## 129 0.11958600 Str agree
## 130 0.12365312 Str agree
## 131 0.12783849 Str agree
## 132 0.13214415 Str agree
## 133 0.13657212 Str agree
## 134 0.14112434 Str agree
## 135 0.14580268 Str agree
## 136 0.15060890 Str agree
## 137 0.15554471 Str agree
## 138 0.16061169 Str agree
## 139 0.16581132 Str agree
## 140 0.17114496 Str agree
## 141 0.17661384 Str agree
## 142 0.18221906 Str agree
## 143 0.18796157 Str agree
## 144 0.19384215 Str agree
## 145 0.19986142 Str agree
## 146 0.20601985 Str agree
## 147 0.21231768 Str agree
## 148 0.21875499 Str agree
## 149 0.22533164 Disag
## 150 0.23204728 Disag
## 151 0.23890135 Disag
## 152 0.24589305 Disag
## 153 0.25302134 Disag
## 154 0.26028495 Disag
## 155 0.26768236 Disag
## 156 0.27521178 Disag
## 157 0.28287119 Disag
## 158 0.29065828 Disag
## 159 0.29857049 Disag
## 160 0.30660498 Str disag
## 161 0.31475866 Str disag
## 162 0.32302816 Str disag
## 163 0.33140985 Str disag
## 164 0.33989982 Str disag
## 165 0.34849392 Str disag
## 166 0.35718773 Str disag
## 167 0.36597660 Str disag
## 168 0.37485561 Str disag
## 169 0.38381963 Str disag
## 170 0.39286330 Str disag
## 171 0.40198104 Str disag
## 172 0.41116709 Str disag
## 173 0.42041547 Str disag
## 174 0.42972007 Str disag
## 175 0.43907460 Str disag
## 176 0.44847262 Str disag
## 177 0.45790758 Str disag
## 178 0.46737283 Str disag
## 179 0.47686163 Str disag
## 180 0.48636715 Str disag
## 181 0.49588255 Str disag
## 182 0.50540093 Str disag
## 183 0.51491540 Str disag
## 184 0.52441907 Str disag
## 185 0.53390508 Str disag
## 186 0.54336664 Str disag
## 187 0.55279701 Str disag
## 188 0.56218954 Str disag
## 189 0.57153771 Str disag
## 190 0.58083509 Str disag
## 191 0.59007543 Str disag
## 192 0.59925260 Str disag
## 193 0.60836069 Str disag
## 194 0.61739394 Str disag
## 195 0.62634680 Str disag
## 196 0.63521395 Str disag
## 197 0.64399028 Str disag
## 198 0.65267092 Str disag
## 199 0.66125123 Str disag
## 200 0.66972683 Str disag
## 201 0.04468304 Str agree
## 202 0.04633679 Str agree
## 203 0.04804866 Str agree
## 204 0.04982048 Str agree
## 205 0.05165408 Str agree
## 206 0.05355137 Str agree
## 207 0.05551426 Str agree
## 208 0.05754473 Str agree
## 209 0.05964477 Str agree
## 210 0.06181643 Str agree
## 211 0.06406177 Str agree
## 212 0.06638289 Str agree
## 213 0.06878194 Str agree
## 214 0.07126107 Str agree
## 215 0.07382247 Str agree
## 216 0.07646836 Str agree
## 217 0.07920097 Str agree
## 218 0.08202255 Str agree
## 219 0.08493539 Str agree
## 220 0.08794176 Str agree
## 221 0.09104395 Str agree
## 222 0.09424427 Str agree
## 223 0.09754501 Str agree
## 224 0.10094847 Str agree
## 225 0.10445694 Str agree
## 226 0.10807268 Str agree
## 227 0.11179796 Str agree
## 228 0.11563500 Str agree
## 229 0.11958600 Str agree
## 230 0.12365312 Str agree
## 231 0.12783849 Str agree
## 232 0.13214415 Str agree
## 233 0.13657212 Str agree
## 234 0.14112434 Str agree
## 235 0.14580268 Str agree
## 236 0.15060890 Str agree
## 237 0.15554471 Str agree
## 238 0.16061169 Str agree
## 239 0.16581132 Str agree
## 240 0.17114496 Str agree
## 241 0.17661384 Str agree
## 242 0.18221906 Str agree
## 243 0.18796157 Str agree
## 244 0.19384215 Str agree
## 245 0.19986142 Str agree
## 246 0.20601985 Str agree
## 247 0.21231768 Str agree
## 248 0.21875499 Str agree
## 249 0.22533164 Disag
## 250 0.23204728 Disag
## 251 0.23890135 Disag
## 252 0.24589305 Disag
## 253 0.25302134 Disag
## 254 0.26028495 Disag
## 255 0.26768236 Disag
## 256 0.27521178 Disag
## 257 0.28287119 Disag
## 258 0.29065828 Disag
## 259 0.29857049 Disag
## 260 0.30660498 Str disag
## 261 0.31475866 Str disag
## 262 0.32302816 Str disag
## 263 0.33140985 Str disag
## 264 0.33989982 Str disag
## 265 0.34849392 Str disag
## 266 0.35718773 Str disag
## 267 0.36597660 Str disag
## 268 0.37485561 Str disag
## 269 0.38381963 Str disag
## 270 0.39286330 Str disag
## 271 0.40198104 Str disag
## 272 0.41116709 Str disag
## 273 0.42041547 Str disag
## 274 0.42972007 Str disag
## 275 0.43907460 Str disag
## 276 0.44847262 Str disag
## 277 0.45790758 Str disag
## 278 0.46737283 Str disag
## 279 0.47686163 Str disag
## 280 0.48636715 Str disag
## 281 0.49588255 Str disag
## 282 0.50540093 Str disag
## 283 0.51491540 Str disag
## 284 0.52441907 Str disag
## 285 0.53390508 Str disag
## 286 0.54336664 Str disag
## 287 0.55279701 Str disag
## 288 0.56218954 Str disag
## 289 0.57153771 Str disag
## 290 0.58083509 Str disag
## 291 0.59007543 Str disag
## 292 0.59925260 Str disag
## 293 0.60836069 Str disag
## 294 0.61739394 Str disag
## 295 0.62634680 Str disag
## 296 0.63521395 Str disag
## 297 0.64399028 Str disag
## 298 0.65267092 Str disag
## 299 0.66125123 Str disag
## 300 0.66972683 Str disag
## 301 0.04468304 Str agree
## 302 0.04633679 Str agree
## 303 0.04804866 Str agree
## 304 0.04982048 Str agree
## 305 0.05165408 Str agree
## 306 0.05355137 Str agree
## 307 0.05551426 Str agree
## 308 0.05754473 Str agree
## 309 0.05964477 Str agree
## 310 0.06181643 Str agree
## 311 0.06406177 Str agree
## 312 0.06638289 Str agree
## 313 0.06878194 Str agree
## 314 0.07126107 Str agree
## 315 0.07382247 Str agree
## 316 0.07646836 Str agree
## 317 0.07920097 Str agree
## 318 0.08202255 Str agree
## 319 0.08493539 Str agree
## 320 0.08794176 Str agree
## 321 0.09104395 Str agree
## 322 0.09424427 Str agree
## 323 0.09754501 Str agree
## 324 0.10094847 Str agree
## 325 0.10445694 Str agree
## 326 0.10807268 Str agree
## 327 0.11179796 Str agree
## 328 0.11563500 Str agree
## 329 0.11958600 Str agree
## 330 0.12365312 Str agree
## 331 0.12783849 Str agree
## 332 0.13214415 Str agree
## 333 0.13657212 Str agree
## 334 0.14112434 Str agree
## 335 0.14580268 Str agree
## 336 0.15060890 Str agree
## 337 0.15554471 Str agree
## 338 0.16061169 Str agree
## 339 0.16581132 Str agree
## 340 0.17114496 Str agree
## 341 0.17661384 Str agree
## 342 0.18221906 Str agree
## 343 0.18796157 Str agree
## 344 0.19384215 Str agree
## 345 0.19986142 Str agree
## 346 0.20601985 Str agree
## 347 0.21231768 Str agree
## 348 0.21875499 Str agree
## 349 0.22533164 Disag
## 350 0.23204728 Disag
## 351 0.23890135 Disag
## 352 0.24589305 Disag
## 353 0.25302134 Disag
## 354 0.26028495 Disag
## 355 0.26768236 Disag
## 356 0.27521178 Disag
## 357 0.28287119 Disag
## 358 0.29065828 Disag
## 359 0.29857049 Disag
## 360 0.30660498 Str disag
## 361 0.31475866 Str disag
## 362 0.32302816 Str disag
## 363 0.33140985 Str disag
## 364 0.33989982 Str disag
## 365 0.34849392 Str disag
## 366 0.35718773 Str disag
## 367 0.36597660 Str disag
## 368 0.37485561 Str disag
## 369 0.38381963 Str disag
## 370 0.39286330 Str disag
## 371 0.40198104 Str disag
## 372 0.41116709 Str disag
## 373 0.42041547 Str disag
## 374 0.42972007 Str disag
## 375 0.43907460 Str disag
## 376 0.44847262 Str disag
## 377 0.45790758 Str disag
## 378 0.46737283 Str disag
## 379 0.47686163 Str disag
## 380 0.48636715 Str disag
## 381 0.49588255 Str disag
## 382 0.50540093 Str disag
## 383 0.51491540 Str disag
## 384 0.52441907 Str disag
## 385 0.53390508 Str disag
## 386 0.54336664 Str disag
## 387 0.55279701 Str disag
## 388 0.56218954 Str disag
## 389 0.57153771 Str disag
## 390 0.58083509 Str disag
## 391 0.59007543 Str disag
## 392 0.59925260 Str disag
## 393 0.60836069 Str disag
## 394 0.61739394 Str disag
## 395 0.62634680 Str disag
## 396 0.63521395 Str disag
## 397 0.64399028 Str disag
## 398 0.65267092 Str disag
## 399 0.66125123 Str disag
## 400 0.66972683 Str disag
## Plot for probability
# x1
p<-ggplot(lnewdat, aes(x=x1, y=Probability, group=Level)) +
geom_line(aes(color=Level))+
geom_point(aes(color=Level))
p
############################################################
### Conditional logit data analysis example: Travel Mode ###
############################################################
# Number of obs: 840
# mode = air/ train/ bus/ car
# choice = yes/ no
# wait = terminal waiting time for plane, train and bus (minutes); 0 for car
# vcost = in vehicle cost for all stages (dollars)
# travel = travel time (in-vehicle time) for all stages (minutes)
# gcst = generalized cost measure: invc+(invc*value of travel time savings)(dollars)
# income = household income ($1000s)
# size = traveling group size in mode chosen (number)
## Load package and data
library(mlogit)
## Warning: package 'mlogit' was built under R version 4.1.1
## Loading required package: dfidx
## Warning: package 'dfidx' was built under R version 4.1.1
##
## Attaching package: 'dfidx'
## The following object is masked from 'package:MASS':
##
## select
## The following object is masked from 'package:stats':
##
## filter
data("TravelMode",package="AER")
summary(cl.TM <- mlogit(choice ~ wait + vcost + travel, TravelMode))
##
## Call:
## mlogit(formula = choice ~ wait + vcost + travel, data = TravelMode,
## method = "nr")
##
## Frequencies of alternatives:choice
## air train bus car
## 0.27619 0.30000 0.14286 0.28095
##
## nr method
## 5 iterations, 0h:0m:0s
## g'(-H)^-1g = 0.000192
## successive function values within tolerance limits
##
## Coefficients :
## Estimate Std. Error z-value Pr(>|z|)
## (Intercept):train -0.78666667 0.60260733 -1.3054 0.19174
## (Intercept):bus -1.43363372 0.68071345 -2.1061 0.03520 *
## (Intercept):car -4.73985647 0.86753178 -5.4636 4.665e-08 ***
## wait -0.09688675 0.01034202 -9.3683 < 2.2e-16 ***
## vcost -0.01391160 0.00665133 -2.0916 0.03648 *
## travel -0.00399468 0.00084915 -4.7043 2.547e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Log-Likelihood: -192.89
## McFadden R^2: 0.32024
## Likelihood ratio test : chisq = 181.74 (p.value = < 2.22e-16)