-
Notifications
You must be signed in to change notification settings - Fork 0
/
final v9.Rmd
510 lines (414 loc) · 17 KB
/
final v9.Rmd
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
---
title: "Buy Online Pick Up in Store (BOPS)"
author: "Kevin, Ram, Ryo"
date: "June 6, 2017"
output:
slidy_presentation: default
ioslides_presentation: default
---
```{r echo=FALSE, warning=FALSE, message=FALSE}
setwd("C:/Users/ktseng/Dropbox/SCU/OMIS 3392/project")
# Assessing the impact of buy-online-pick up-in store strategy on online and Brick-and-mortar store sales and returns
```
```{r echo=FALSE, warning=FALSE, message=FALSE}
## Load Data Set
library(data.table)
library(readr)
library(dplyr)
library(VIF)
library(usdm)
library(AER)
library(foreign)
bops <- read_csv("C:/Users/ktseng/Dropbox/SCU/OMIS 3392/project/data.txt")
bops <- as.data.table(bops)
bops2012 <- fread("C:/Users/ktseng/Dropbox/SCU/OMIS 3392/project/BOPS-FY12.csv")
bops2013 <- fread("C:/Users/ktseng/Dropbox/SCU/OMIS 3392/project/BOPS-FY13.csv")
# bops - original data file
# bops1 - used for returns model
# bops2 - used for sales model
# bops3 - sales model for store 2 and 6
```
```{r echo=FALSE, warning=FALSE, message=FALSE}
bops$gender[is.na(bops$gender)] <- "U"
```
```{r echo=FALSE, warning=FALSE, message=FALSE}
bops$homeowner_code[bops$homeowner_code == "R"] <- 0
bops$homeowner_code[bops$homeowner_code == "O"] <- 1
```
```{r echo=FALSE, warning=FALSE, message=FALSE}
bops$store_number <- as.factor(bops$store_number)
bops <- within(bops, store_number <- relevel(store_number, ref = 3))
```
```{r echo=FALSE, warning=FALSE, message=FALSE}
# Multiple plot function
#
# ggplot objects can be passed in ..., or to plotlist (as a list of ggplot objects)
# - cols: Number of columns in layout
# - layout: A matrix specifying the layout. If present, 'cols' is ignored.
#
# If the layout is something like matrix(c(1,2,3,3), nrow=2, byrow=TRUE),
# then plot 1 will go in the upper left, 2 will go in the upper right, and
# 3 will go all the way across the bottom.
#
multiplot <- function(..., plotlist=NULL, file, cols=1, layout=NULL) {
library(grid)
# Make a list from the ... arguments and plotlist
plots <- c(list(...), plotlist)
numPlots = length(plots)
# If layout is NULL, then use 'cols' to determine layout
if (is.null(layout)) {
# Make the panel
# ncol: Number of columns of plots
# nrow: Number of rows needed, calculated from # of cols
layout <- matrix(seq(1, cols * ceiling(numPlots/cols)),
ncol = cols, nrow = ceiling(numPlots/cols))
}
if (numPlots==1) {
print(plots[[1]])
} else {
# Set up the page
grid.newpage()
pushViewport(viewport(layout = grid.layout(nrow(layout), ncol(layout))))
# Make each plot, in the correct location
for (i in 1:numPlots) {
# Get the i,j matrix positions of the regions that contain this subplot
matchidx <- as.data.frame(which(layout == i, arr.ind = TRUE))
print(plots[[i]], vp = viewport(layout.pos.row = matchidx$row,
layout.pos.col = matchidx$col))
}
}
}
```
# Visualization of Variables
```{r echo=FALSE, warning=FALSE, message=FALSE}
## Normality Check
library(ggplot2)
p1 <- ggplot(bops, aes(x=net_purchase_amount)) +
geom_histogram()
p2 <- ggplot(bops, aes(x=age_band))+
geom_histogram()
p3 <-ggplot(bops, aes(x=est_income_code))+
geom_histogram()
p4 <-ggplot(bops, aes(x=length_of_residence))+
geom_histogram()
p8 <-ggplot(bops, aes(x=summary))+
geom_bar()
p9 <-ggplot(bops, aes(x=child))+
geom_bar(width=0.3)
p10 <-ggplot(bops, aes(x=homeowner_code))+
geom_bar(width=0.3)
p11 <-ggplot(bops, aes(x=ethnic_code))+
geom_bar(width=0.3)
p12 <-ggplot(bops, aes(x=year)) +
geom_bar(width=0.3)
multiplot(p1, p2, p3,p4,p8, p9, p10, p11, p12, cols=3)
```
# Goal 1: Store Sales
**Purpose**: Assess the impact of the BOPS strategy on store sales
**Primary Independent Variable**: BOPS (dummy variable)
0 - mail
1 - store pickup
**Secondary Independent Variable**: Store Number
As the purpose states, we want to assess impact at the store level.
**Control Variables**:
log(net_puchase_amount)*
gender
age_band
est_income_code
ethnic_code
**Dependent Variable**: Transaction Count (generated variable)
* Why is net_purchase_amount not a sufficient dependent variable?
Will look at the program 1 year before and 1 year after the start.
**Unused Variables**:
transaction_id
customer_id
purchase_date
sku
return_date
return_store
time_to_return
homeowner_code
length_of_residence
child
year
month_index
summary
# Data Cleaning for sales model
## Create BOPS dummy variable
Data was originaly given in two seperate files and so we have to merge them.
0 = Purchase in store
1 = Purchase online
```{r echo=FALSE, warning=FALSE, message=FALSE}
# Add column to the individual years
bops2012 <- bops2012[,-c(1,3)]
bops2012 <- cbind(bops2012, b2012 = 1)
bops2013 <- bops2013[,-c(1,3)]
bops2013 <- cbind(bops2013, b2013 = 1)
# Merge dataframes
bops <- merge(bops, bops2012, by="transaction_id", all.x=TRUE)
bops <- merge(bops, bops2013, by="transaction_id", all.x=TRUE)
# fill in NA
bops$b2012[is.na(bops$b2012)] <- 0
bops$b2013[is.na(bops$b2013)] <- 0
#merge the 2 columns
bops$bops <- bops$b2012 + bops$b2013
bops$gender <- as.factor(bops$gender)
bops$ethnic_code <- as.factor(bops$ethnic_code)
```
```{r echo=FALSE, warning=FALSE, message=FALSE}
bops2 <- bops[,-c(3,6:10,18:19, 22:23)]
```
## Filter out customers with only 1 transaction
We are primarily concerned with return customers and not one time only customers.
```{r echo=FALSE, warning=FALSE, message=FALSE}
bops2$customer_id <- as.factor(bops2$customer_id)
bops2a <- bops2[which(bops2$month_index <= 24),]
bops2b <- bops2[which(bops2$month_index <= 36 & bops2$month_index >= 25),]
# determine duplicates
a = count(bops2a, customer_id)
bops2a <- merge(bops2a, a, by="customer_id", all.x=TRUE)
bops2a <- bops2a[which(bops2a$n >= 2),]
bops2a <- bops2a %>%
group_by(customer_id) %>%
summarise(net_purchase_amount = sum(net_purchase_amount), store_number = first(store_number), gender = first(gender), age_band = first(age_band), est_income_code = first(est_income_code), ethnic_code = first(ethnic_code), bops = first(bops), numitems = first(n), homeowner_code = first(homeowner_code), length_of_residence = first(length_of_residence), child = first(child))
a = count(bops2b, customer_id)
bops2b <- merge(bops2b, a, by="customer_id", all.x=TRUE)
bops2b <- bops2b[which(bops2b$n >= 2),]
bops2b <- bops2b %>%
group_by(customer_id) %>%
summarise(net_purchase_amount = sum(net_purchase_amount), store_number = first(store_number), gender = first(gender), age_band = first(age_band), est_income_code = first(est_income_code), ethnic_code = first(ethnic_code), bops = first(bops), numitems = first(n), homeowner_code = first(homeowner_code), length_of_residence = first(length_of_residence), child = first(child))
bops2 <- rbind(bops2a, bops2b)
cat("From our original set of", nrow(bops), "data points, we are left with", nrow(bops2), "data points.")
```
## Data points that are missing information
```{r echo=FALSE, warning=FALSE, message=FALSE}
bops2$missing_data <- 0
bops2$missing_data <- rowSums(is.na(bops2))
table(bops2$missing_data)
```
Confirm that we will not lose too much data due to NA.
## net_purchase_amount (log)
```{r echo=FALSE, warning=FALSE, message=FALSE}
cat("Number of na entries:", sum(is.na(bops$net_purchase_amount)))
bops2$net_purchase_amount <- log(bops2$net_purchase_amount+1)
p1 <- ggplot(bops, aes(x=net_purchase_amount)) +
geom_histogram()
p2 <- ggplot(bops2, aes(x=net_purchase_amount))+
geom_histogram()
multiplot(p1, p2, cols=2)
```
```{r echo=FALSE, warning=FALSE, message=FALSE}
bops3 <- bops2[!(bops2$store_number == "5998"),]
bops3 <- within(bops3, store_number <- relevel(store_number, ref = 3))
```
# Sales Model 1 OLS (2+ items purchased)
```{r echo=FALSE, warning=FALSE, message=FALSE}
sales1 <- lm(numitems ~ bops + store_number + net_purchase_amount + gender + age_band + est_income_code + ethnic_code, data=bops3)
summary(sales1)
```
# Sales Model with Interaction (2+ items purchased)
We want to see the effect on stores.
```{r echo=FALSE, warning=FALSE, message=FALSE}
sales2 <- lm(numitems ~ bops * store_number + net_purchase_amount + gender + age_band + est_income_code + ethnic_code, data=bops3)
summary(sales2)
```
## Comparison of the two models (nested)
```{r echo=FALSE, warning=FALSE, message=FALSE}
anova(sales1, sales2, test="Chisq")
```
# Poisson
```{r echo=FALSE, warning=FALSE, message=FALSE}
poisson1 <- glm(numitems ~ bops * store_number + net_purchase_amount + gender + age_band + est_income_code + ethnic_code, family="poisson", data=bops3)
summary(poisson1)
```
## Heteroscedasticity test and IRRs
```{r echo=FALSE, warning=FALSE, message=FALSE}
library(lmtest)
gqtest(poisson1)
bptest(poisson1)
```
Both tests are significant therefore we have heteroscedasticity.
## Huber-White robust standard errors
```{r echo=FALSE, warning=FALSE, message=FALSE}
f <- as.data.frame(coeftest(poisson1, vcov = vcovHC(poisson1, "HC1"))[,-c(2,3)])
f <- cbind(summary(poisson1)$coefficients[,-c(2,3)], f)
colnames(f) <- c("Orig Est", "Pr(>|z|)", "Std Errors Est", "Pr(>|z|)")
f[,2][f[,2] <= 0.05] <- "***"
f[,2][f[,2] >= 0.05] <- ""
f[,4][f[,4] <= 0.05] <- "***"
f[,4][f[,4] >= 0.05] <- ""
f
```
bops and store number are still significant.
```{r echo=FALSE, warning=FALSE, message=FALSE}
exp(coef(poisson1)) # We see that the incident rate for facebookvisit is 1.083 times the incident rate for the no facebookvisit. Customers who visit Facebook before Amazon purchase 8.3% more than customers who visit Amazon.com directly.
```
## Model fit test
```{r echo=FALSE, warning=FALSE, message=FALSE}
cat("Chi-squared test statistic:", with(poisson1, null.deviance - deviance))
cat("Degrees of freedom:", with(poisson1, df.null - df.residual))
cat("P value:", with(poisson1, pchisq(null.deviance - deviance, df.null - df.residual, lower.tail = FALSE)))
```
Horrible fit
# Negative Binomial model
```{r echo=FALSE, warning=FALSE, message=FALSE}
library(foreign)
library(MASS)
summary(negbin1 <- glm.nb(numitems ~ bops * store_number + net_purchase_amount + gender + age_band + est_income_code + ethnic_code, data = bops3))
```
## Heteroscedasticity
```{r echo=FALSE, warning=FALSE, message=FALSE}
gqtest(negbin1)
bptest(negbin1)
e <- as.data.frame(coeftest(negbin1, vcov = vcovHC(negbin1, "HC1"))[,-c(2,3)])
e <- cbind(summary(negbin1)$coefficients[,-c(2,3)], e)
colnames(e) <- c("Orig Est", "Pr(>|z|)", "Std Errors Est", "Pr(>|z|)")
e[,2][e[,2] <= 0.05] <- "***"
e[,2][e[,2] >= 0.05] <- ""
e[,4][e[,4] <= 0.05] <- "***"
e[,4][e[,4] >= 0.05] <- ""
e
```
## Test model fit
```{r echo=FALSE, warning=FALSE, message=FALSE}
cat("Chi-squared test statistic:", with(negbin1, null.deviance - deviance))
cat("Degrees of freedom:", with(negbin1, df.null - df.residual))
cat("P value:", with(negbin1, pchisq(null.deviance - deviance, df.null - df.residual, lower.tail = FALSE)))
```
Model fits the data since the test is significant
## Compare Poisson regression to Negative Binomial regression
Chisq Test
```{r echo=FALSE, warning=FALSE, message=FALSE}
X2 <- 2 * (logLik(negbin1) - logLik(poisson1))
X2
pchisq(X2, df = 1, lower.tail=FALSE)
```
Negative Binomial is more appropriate than Poisson since there is over-dispersion.
# Sales Model Summary
Final Model: Negative Binomial
numitems ~ bops * store_number + net_purchase_amount + gender + age_band + est_income_code + ethnic_code
```{r echo=FALSE, warning=FALSE, message=FALSE}
library(effects)
plot(effect(term="bops:store_number", mod=negbin1, default.levels=2),multiline=TRUE)
```
```{r echo=FALSE, warning=FALSE, message=FALSE, results = 'asis'}
library(knitr)
z <- matrix(c("$170", "$146", "75,000", "6,500", "1.5", "0.6", "$19,125,000", "$569,400"), ncol=4)
colnames(z) <- c("Mean Transaction Price", "Number of Customer", "Transaction Increase", "Total Sales Increase")
rownames(z) <- c(2, 6)
kable(z, caption = "Sales Increase")
```
# Goal 2: Store Returns
**Purpose**: Assess the impact of the BOPS strategy on store returns
**Dependent Variable**: return (dummy variable)
0 - Item has not been returned
1 - Item has been returned
**Primary Independent Variable**: BOPS (dummy variable)
0 - mail
1 - store pickup
**Secondary Independent Variable**: Store Number
As the purpose states, we want to assess impact at the store level.
**Control Variables**:
log(net_puchase_amount)
gender
age_band
est_income_code
ethnic_code
month
summary *
# Data Cleaning for returns model
## Data points that are missing information
```{r echo=FALSE, warning=FALSE, message=FALSE}
bops1 <- bops[,-c(3, 6, 8:10, 20, 22:23)]
bops1$missing_data <- 0
bops1$missing_data <- rowSums(is.na(bops1))
table(bops1$missing_data)
```
## net_purchase_amount (log)
```{r echo=FALSE, warning=FALSE, message=FALSE}
library(ggplot2)
cat("Number of na entries:", sum(is.na(bops$net_purchase_amount)))
bops1$net_purchase_amount <- log(bops1$net_purchase_amount+1)
p1 <- ggplot(bops, aes(x=net_purchase_amount)) +
geom_histogram()
p2 <- ggplot(bops1, aes(x=net_purchase_amount))+
geom_histogram()
multiplot(p1, p2, cols=2)
```
```{r echo=FALSE, warning=FALSE, message=FALSE}
returns1 <- bops1
returns1$summary <- as.factor(returns1$summary)
```
# Returns Model 1 OLS
```{r echo=FALSE, warning=FALSE, message=FALSE}
retmodel1 <- lm(return ~ bops + store_number + net_purchase_amount + gender + age_band + est_income_code + ethnic_code + month + summary, data=returns1)
summary(retmodel1)
```
```{r echo=FALSE, warning=FALSE, message=FALSE}
#dfret1=data.frame(returns1$bops,returns1$net_purchase_amount,returns1$age_band,returns1$est_income_code)
#vif(dfret1)
```
# Returns Model 2 OLS (interaction with store_number)
```{r echo=FALSE, warning=FALSE, message=FALSE}
retmodel2 <- lm(return ~ bops * store_number + net_purchase_amount + gender + age_band + est_income_code + ethnic_code + month+ summary, data=returns1)
summary(retmodel2)
```
## Comparison of models
```{r echo=FALSE, warning=FALSE, message=FALSE}
anova(retmodel1,retmodel2,test="Chisq")
```
Model with interaction variable is better
## Range of Returns Model 2
```{r echo=FALSE, warning=FALSE, message=FALSE}
predictedprobability_lm<-predict(retmodel2)
#Range along is sufficient to explain why we have to switch to Logit model.
range(predictedprobability_lm)
library(aod)
library(Rcpp)
```
We expect the results to be between 0 and 1. However it is out of bounds.
#Logit Model
## Satisfaction of Logit Requirements
```{r echo=FALSE, warning=FALSE, message=FALSE}
table(returns1$return)
```
## Model
```{r echo=FALSE, warning=FALSE, message=FALSE}
returns1$gender <- as.factor(returns1$gender)
returns1$ethnic_code <- as.factor(returns1$ethnic_code)
returns1$month <- as.factor(returns1$month)
logit1<- glm(return ~ bops * store_number + net_purchase_amount + gender + age_band + est_income_code + ethnic_code + month+ summary, data=returns1, family="binomial")
summary(logit1)
```
# Marginal Effect
```{r echo=FALSE, warning=FALSE, message=FALSE}
library(mfx)
#Rule of thumb, we always assume heterskedasticity is present, thus we use robust standard error to adjust standard errors for independent variables.
b <- logitmfx(formula=return ~ bops * store_number + net_purchase_amount + gender + age_band + est_income_code + ethnic_code + month+ summary, data=returns1, robust=TRUE)
b
```
#Comparison with Probit model (marginal effects)
```{r echo=FALSE, warning=FALSE, message=FALSE}
probit1<- glm(return ~ bops * store_number + net_purchase_amount + gender + age_band + est_income_code + ethnic_code + month+ summary, data=returns1, family=binomial(link="probit"))
c <- probitmfx(formula=return ~ bops * store_number + net_purchase_amount + gender + age_band + est_income_code + ethnic_code + month+ summary, data=returns1, robust=TRUE)
a <- as.data.frame(b$mfxest[,1])
a <- cbind(a, c$mfxest[,1])
colnames(a) <- c("logit", "probit")
a
```
# Endogenity
```{r echo=FALSE, warning=FALSE, message=FALSE}
returns1$child <- as.numeric(returns1$child)
returns1$homeowner_code <- as.numeric(returns1$homeowner_code)
df=data.frame(returns1$return, returns1$bops, returns1$homeowner_code, returns1$length_of_residence, returns1$child)
cor(df, use="pairwise.complete.obs")[,1:2]
```
```{r echo=FALSE, warning=FALSE, message=FALSE}
## 2SLS with 2 instruments (homeowner_code + length_of_residence)
#sls2 <- ivreg(return ~ bops * store_number + net_purchase_amount + gender + age_band + est_income_code + ethnic_code + month + summary | homeowner_code + length_of_residence + store_number + net_purchase_amount + gender + age_band + est_income_code + ethnic_code + month + summary, data = returns1)
#summary(sls2,diagnostics=TRUE)
```
# Summary
```{r echo=FALSE, warning=FALSE, message=FALSE}
plot(effect(term="bops:store_number", mod=logit1, default.levels=3),multiline=TRUE)
```