Fattorel Marta & Tonin Marco
This situation inevitably enhances the necessity of real estate agencies or private people to understand customer preferences, in order to find tenants for the rooms or the apartments they have.
The aim of this Choice-based Conjoint Analysis is to investigate customer preferences about student accommodation according to four different attributes:
- typology: ‘single’; ‘shared/double’
- position (distance from the university): ‘<500m’; ‘500m - 1.5km’; ‘>1.5km’
- number of tenants: ‘2’; ‘3-4’; ‘5-6’
- facilities: ‘living-room’; ‘balcony in the room’; ‘dishwasher and microwave’
- prices (in euros): ‘250’, ‘350’, ‘450’
Moreover, the research tries to analyse the preference share of Marta’s room with respect to other seven product profiles found in the Facebook group ‘AAA Appartamenti studenti Trento’, which represents the student accommodation market nowadays.
To sum up, the questions this research has the aim to answer are:
-
Which room’s features are considered the most important by students? Which attributes’ levels are associated with a positive part worth?
-
How can we assess the preference of a specific product profile we want to launch on the market? How can we increase its success?
-
Are students’ preferences homogeneous towards the choice of the room?
The choice-based conjoint survey uses a Fractional Factorial Design with a Mix and Match approach. This permits to have a fraction of all the possible profiles, respecting orthogonality, avoiding potentially dangerous patterns the rotation method has, while keeping a small number of questions. However, in this way it is not possible to assess the combined effects of the attributes.
Given the high number of questions, we have decided to divide the choice-based survey into 2 blocks, both with 9 questions with 3 alternatives each.
In addition to the attributes mentioned in the introduction, the survey provides us some individual information:
- year of birth
- sex
- degree
- if they live in the city or they reach it with means of transport (fuori sede/pendolare)
The two surveys have been created and distributed through the ‘Google Moduli’ platform [1]. The sample design follows a snowball sampling, in which existing study subjects recruit future subjects among their acquaintances. We have considered only university students (Master’s, Bachelor’s and PhD).
Load necessary libraries
library(data.table)
library(ggplot2)
library(ggpubr)
library(support.CEs)
library(tidyverse)
library(mlogit)
library(parallel)
library(MASS)
library(lattice)Build the survey using a fractional factorial design and a mix and match approach.
attrib <- list(TIPOLOGIA = c("singola", "doppia"),
POSIZIONE = c("meno di 500m", "500m - 1.5km", "più di 1.5km"),
INQUILINI = c("2", "3-4", "5-6"),
SERVIZI = c("soggiorno", "balconcino in camera", "lavastoviglie e microonde"),
PREZZO = c(250, 350, 450))
MMSurvey <- rotation.design(attribute.names=attrib,
nalternatives=3,
nblocks=2, # 9 questions per block
randomize=TRUE, # mix and match approach
seed=999) # for reproducibility
# MMSurvey
# questionnaire(MMSurvey) Organize the questionnaire in a dataframe format.
MMSurveyDF <- NULL
nalt <- MMSurvey$design.information$nalternatives
for(i in seq(1:nalt)) {
MMSurveyDF <- rbind(MMSurveyDF, MMSurvey$alternatives[[i]])
}
MMSurveyDF <- MMSurveyDF[order(MMSurveyDF$BLOCK, MMSurveyDF$QES),]
head(MMSurveyDF)## BLOCK QES ALT TIPOLOGIA POSIZIONE INQUILINI SERVIZI
## 1 1 1 1 singola più di 1.5km 2 lavastoviglie e microonde
## 19 1 1 2 doppia 500m - 1.5km 3-4 balconcino in camera
## 37 1 1 3 singola più di 1.5km 5-6 lavastoviglie e microonde
## 2 1 2 1 singola meno di 500m 2 balconcino in camera
## 20 1 2 2 doppia 500m - 1.5km 3-4 lavastoviglie e microonde
## 38 1 2 3 singola più di 1.5km 5-6 soggiorno
## PREZZO
## 1 350
## 19 350
## 37 450
## 2 350
## 20 450
## 38 250
Load the files ‘block1.csv’ and ‘block2.csv’, which contain the data of the two blocks of the survey. They have been downloaded from ‘Google Moduli’. In particular, block 1 counts 74 respondents of which 2 have been removed because they are not university students, while block 2 counts 70 respondents. Therefore, our sample is composed of 142 university students.
Data have been merged, renaming the columns.
resp1 <- read.csv('block1.csv')
resp2 <- read.csv('block2.csv')
resp1$BLOCK <- 1
resp2$BLOCK <- 2
# Merge the blocks
resp <- rbind(resp1, resp2)
# Rename columns
resp <- resp %>% rename("ANNO" = "Anno.di.nascita.",
"SESSO" = "Sesso.",
"FUORISEDE_PENDOLARE" = "Sei.studente.studentessa.",
"LAUREA" = "Sei.studente.studentessa..1",
"Q1" = "Scegli.il.profilo.che.preferisci.",
"Q2" = "Scegli.il.profilo.che.preferisci..1",
"Q3" = "Scegli.il.profilo.che.preferisci..2",
"Q4" = "Scegli.il.profilo.che.preferisci..3",
"Q5" = "Scegli.il.profilo.che.preferisci..4",
"Q6" = "Scegli.il.profilo.che.preferisci..5",
"Q7" = "Scegli.il.profilo.che.preferisci..6",
"Q8" = "Scegli.il.profilo.che.preferisci..7",
"Q9" = "Scegli.il.profilo.che.preferisci..8")
# Rename profiles
resp[resp == 'Profilo 1'] <- 1
resp[resp == 'Profilo 2'] <- 2
resp[resp == 'Profilo 3'] <- 3
# Remove timestamp
resp$Informazioni.cronologiche <- NULL
resp$ID <- seq.int(nrow(resp))
# Remove non students
resp <- resp[!resp$FUORISEDE_PENDOLARE == "non sono studente/studentessa",]The function make.dataset() of the package support.CEs allows us to
create a dataset with information about the survey and the responses.
# Create Dataset
dataset <- make.dataset(respondent.dataset = resp,
choice.indicators = c("Q1", "Q2", "Q3", "Q4", "Q5",
"Q6", "Q7", "Q8", "Q9"),
design.matrix = MMSurveyDF)
dataset$RES[dataset$RES == TRUE] <- 1
dataset <- dataset[c('ID', 'QES', 'ALT', 'BLOCK', 'TIPOLOGIA', 'POSIZIONE',
'INQUILINI', 'SERVIZI', 'PREZZO', 'SESSO', 'ANNO',
'FUORISEDE_PENDOLARE', 'LAUREA',
'RES')]# Fix questions number
dataset$QES <- ceiling(as.numeric(rownames(dataset))/3)
# Shorten some df entries names
levels(dataset$SERVIZI) <- c(levels(dataset$SERVIZI), "balconcino", "lav. mic.")
dataset$SERVIZI[dataset$SERVIZI == "balconcino in camera"] <- "balconcino"
dataset$SERVIZI[dataset$SERVIZI == "lavastoviglie e microonde"] <- "lav. mic."
dataset$FUORISEDE_PENDOLARE <- as.factor(dataset$FUORISEDE_PENDOLARE)
levels(dataset$FUORISEDE_PENDOLARE) <- c(levels(dataset$FUORISEDE_PENDOLARE), "< 300km", "> 300km")
dataset$FUORISEDE_PENDOLARE[dataset$FUORISEDE_PENDOLARE %like% "fuorisede entro"] <- "< 300km"
dataset$FUORISEDE_PENDOLARE[dataset$FUORISEDE_PENDOLARE %like% "fuorisede oltre"] <- "> 300km"
levels(dataset$POSIZIONE) <- c(levels(dataset$POSIZIONE), "< 500m", "> 1.5km")
dataset$POSIZIONE[dataset$POSIZIONE == "meno di 500m"] <- "< 500m"
dataset$POSIZIONE[dataset$POSIZIONE == "più di 1.5km"] <- "> 1.5km"
# Save dataframe
write.csv(x=dataset, file="df.csv", row.names=FALSE)In order to gain an overall view of the collected data, we start with an exploratory data analysis. All respondents are repeated the same amount of time, meaning that each of them saw 27 product profiles. Concerning the attributes, the table below shows the frequency for each level of each attribute. All levels are quite balanced.
# Load dataset
dataset <- read.csv("df.csv")
# summary(dataset)
# str(dataset)
# sapply(dataset, function(x) sum(is.na(x))) # no NA values
# Check the number for each id and variable:
# all respondents are repeated the same amount of time (27 product profiles)
# table(dataset$ID)
sapply(dataset[,5:9], table) # small differences due to the different number of responses in the two blocks## $TIPOLOGIA
##
## doppia singola
## 1912 1922
##
## $POSIZIONE
##
## < 500m > 1.5km 500m - 1.5km
## 1272 1280 1282
##
## $INQUILINI
##
## 2 3-4 5-6
## 1278 1274 1282
##
## $SERVIZI
##
## balconcino lav. mic. soggiorno
## 1278 1278 1278
##
## $PREZZO
##
## 250 350 450
## 1282 1276 1276
# Convert into qualitative
dataset$ALT <- as.factor(dataset$ALT)
dataset$ALT <- recode_factor(dataset$ALT, "1" = "first", "2" = "second", "3" = "third")
dataset$PREZZO <- as.factor(dataset$PREZZO)
dataset$ANNO <- as.factor(dataset$ANNO)
# Change levels order
dataset$POSIZIONE <- factor(dataset$POSIZIONE, levels=c("< 500m","500m - 1.5km","> 1.5km"))
dataset$SERVIZI <- factor(dataset$SERVIZI, levels=c("soggiorno","lav. mic.","balconcino"))plot.data(dataset[dataset$RES == 1, 5:13])
The first four plots display some personal features of the respondents.
The majority of them are females, born between 1996 and 1999 and
non-resident in the city where they study. Master’s students exceed
Bachelor’s ones.
The other plots represent the general respondents’ choices: a single
room, close to the university, for 2 students, at the lowest price
appears to be the most popular choice for the attributes. The services
results are quite balanced.
We can start our analysis by fitting a Multinomial Logit model on our
data. The dfidx() function is necessary in order to reshape the data
in the format required by mlogit().
data.mlogit <- dfidx(dataset, idx = list(c("QES", "ID"), "ALT"), drop.index=F,
levels=c("first", "second", "third")) # position of the alternatives
m1 <- mlogit(RES ~ TIPOLOGIA + POSIZIONE + INQUILINI + SERVIZI + PREZZO, data = data.mlogit)
summary(m1)##
## Call:
## mlogit(formula = RES ~ TIPOLOGIA + POSIZIONE + INQUILINI + SERVIZI +
## PREZZO, data = data.mlogit, method = "nr")
##
## Frequencies of alternatives:choice
## first second third
## 0.34429 0.32081 0.33490
##
## nr method
## 6 iterations, 0h:0m:0s
## g'(-H)^-1g = 9.77E-06
## successive function values within tolerance limits
##
## Coefficients :
## Estimate Std. Error z-value Pr(>|z|)
## (Intercept):second -0.0098578 0.0894880 -0.1102 0.912284
## (Intercept):third -0.1041529 0.0872400 -1.1939 0.232530
## TIPOLOGIAsingola 1.6117682 0.1136623 14.1803 < 2.2e-16 ***
## POSIZIONE500m - 1.5km -0.3073381 0.1184303 -2.5951 0.009456 **
## POSIZIONE> 1.5km -1.2448225 0.1337612 -9.3063 < 2.2e-16 ***
## INQUILINI3-4 -0.1842692 0.1039950 -1.7719 0.076410 .
## INQUILINI5-6 -0.9666814 0.1137254 -8.5001 < 2.2e-16 ***
## SERVIZIlav. mic. -0.0269365 0.1117449 -0.2411 0.809514
## SERVIZIbalconcino -0.3513543 0.1244398 -2.8235 0.004750 **
## PREZZO350 -0.6282180 0.0931280 -6.7457 1.522e-11 ***
## PREZZO450 -1.8014886 0.1365246 -13.1953 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Log-Likelihood: -972.16
## McFadden R^2: 0.30732
## Likelihood ratio test : chisq = 862.65 (p.value = < 2.22e-16)
From the coefficient estimates, we notice that both intercepts have a high p-value, meaning that they could be not relevant. In fact, it makes sense that the choices of our respondents are not influenced by the position of the alternatives in the questionnaire. However, before taking any formal decision, we should estimate the Multinomial Logit model without the intercepts and compare its performance with the previous one through a likelihood ratio test.
# model without the intercepts
m2 <- mlogit(RES ~ TIPOLOGIA + POSIZIONE + INQUILINI + SERVIZI
+ PREZZO | -1 , data = data.mlogit)
summary(m2)##
## Call:
## mlogit(formula = RES ~ TIPOLOGIA + POSIZIONE + INQUILINI + SERVIZI +
## PREZZO | -1, data = data.mlogit, method = "nr")
##
## Frequencies of alternatives:choice
## first second third
## 0.34429 0.32081 0.33490
##
## nr method
## 6 iterations, 0h:0m:0s
## g'(-H)^-1g = 2.99E-06
## successive function values within tolerance limits
##
## Coefficients :
## Estimate Std. Error z-value Pr(>|z|)
## TIPOLOGIAsingola 1.611738 0.114229 14.1097 < 2.2e-16 ***
## POSIZIONE500m - 1.5km -0.315874 0.118222 -2.6719 0.007543 **
## POSIZIONE> 1.5km -1.242910 0.129364 -9.6078 < 2.2e-16 ***
## INQUILINI3-4 -0.181471 0.101675 -1.7848 0.074291 .
## INQUILINI5-6 -0.946899 0.111372 -8.5022 < 2.2e-16 ***
## SERVIZIlav. mic. -0.044284 0.111533 -0.3970 0.691333
## SERVIZIbalconcino -0.350181 0.121937 -2.8718 0.004081 **
## PREZZO350 -0.623932 0.092798 -6.7235 1.774e-11 ***
## PREZZO450 -1.767213 0.131306 -13.4588 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Log-Likelihood: -972.99
lrtest(m2, m1)## Likelihood ratio test
##
## Model 1: RES ~ TIPOLOGIA + POSIZIONE + INQUILINI + SERVIZI + PREZZO |
## -1
## Model 2: RES ~ TIPOLOGIA + POSIZIONE + INQUILINI + SERVIZI + PREZZO
## #Df LogLik Df Chisq Pr(>Chisq)
## 1 9 -972.99
## 2 11 -972.16 2 1.6553 0.4371
The likelihood ratio test allows us to confirm that the two models explain equally well the data. In fact, the high p-value tells us that we have no evidence to reject the null hp of no difference in terms of goodness of fit between the two models. Hence, we can use the simpler model, without the intercepts.
Now, let’s verify with another likelihood ratio test if we can consider the attribute price as a quantitative predictor. In this way we would gain two additional degrees of freedom.
m3 <- mlogit(RES ~ TIPOLOGIA + POSIZIONE + INQUILINI + SERVIZI +
as.numeric(as.character(PREZZO)) | -1 , data = data.mlogit)
# summary(m3)lrtest(m3, m2)## Likelihood ratio test
##
## Model 1: RES ~ TIPOLOGIA + POSIZIONE + INQUILINI + SERVIZI + as.numeric(as.character(PREZZO)) |
## -1
## Model 2: RES ~ TIPOLOGIA + POSIZIONE + INQUILINI + SERVIZI + PREZZO |
## -1
## #Df LogLik Df Chisq Pr(>Chisq)
## 1 8 -977.72
## 2 9 -972.99 1 9.4538 0.002107 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
This time, the likelihood ratio test displays a value below 0.01. As a consequence we have evidence to reject the null hp and by looking at the results we can conclude that m2 better fits our data. Hence, we should treat the price as qualitative.
So far, the best model results to be “m2” i.e. the model without the intercepts and with price as a qualitative variable. In addition, by looking at the estimated coefficients we have an estimate of the average part worth for each level with respect to the reference level. The most preferred type of room appears to be: single, close to the university (less than 500m), for 2 students, living room, 250 euros. Typology, position and price seem the most relevant attributes.
Preference share prediction
We can also use the MNL model to obtain preference share predictions. Since Marta is looking for a student who is willing to rent her room, we are going to consider her room as a reference product profile. In particular, the room is single, for 3 students, less than 500m away from the university, with a balcony and it costs 310 euros. Instead, regarding the competitors’ products, we built 7 profiles based on information retrieved from the Facebook group “AAA Appartamenti studenti Trento”.
# Preference share prediction with Bootstrap confidence intervals
source("Bootstrap MNL model.R")
BootCI.predict.mnl(m2, new.data)## share 2.5% 97.5% TIPOLOGIA POSIZIONE INQUILINI
## 98 0.30953630 0.255231966 0.37019145 singola < 500m 3-4
## 70 0.14900139 0.103458676 0.19510459 singola 500m - 1.5km 5-6
## 66 0.12676644 0.096458357 0.16390653 singola > 1.5km 3-4
## 140 0.06231888 0.043612243 0.08513550 singola < 500m 5-6
## 61 0.08766467 0.066326584 0.10841007 doppia < 500m 3-4
## 33 0.05308352 0.032932287 0.07499829 doppia 500m - 1.5km 5-6
## 1 0.19615835 0.149986153 0.24660227 doppia < 500m 2
## 53 0.01547045 0.008936379 0.02478551 doppia > 1.5km 5-6
## SERVIZI PREZZO
## 98 balconcino 350
## 70 soggiorno 350
## 66 soggiorno 350
## 140 lav. mic. 450
## 61 soggiorno 350
## 33 lav. mic. 250
## 1 soggiorno 250
## 53 balconcino 250
The reference profile has the highest preference share, which is around 0.31. This means that on average, respondents are expected to choose it 31% of times.
Now, we are going to plot the sensitivity chart, which shows the expected changes in preference shares due to changes in each attribute of our reference profile.
sensitivity.chart
The most relevant attribute appears to be single room since with a double room the preference share decreases by more than 0.2%. Considering that there are some features that we cannot change such as the position of the room, the number of students that the apartment can host, and the living room, we should think about adding a dishwasher and a microwave (+0.06). The price of the room is lower than 350 euros, however here we had to approximate it to the closest available option. Hence, with 310 euros the preference share would be higher.
To control and analyse consumer heterogeneity, we can estimate a Multinomial Logit Model with random coefficients that vary across customers. This allows us to relax the assumption of homogeneity in customer preferences and to deal with the distribution of values of the parameters that vary across respondents. In this case, we assume that all the coefficients follow a normal distribution.
m2.rpar <- rep("n", length=length(m2$coef)) # coef. follow a normal distr.
names(m2.rpar) <- names(m2$coef)
m2.mixed <- mlogit(RES ~ TIPOLOGIA + POSIZIONE + INQUILINI + SERVIZI + PREZZO | -1 ,
data = data.mlogit, panel=TRUE, rpar = m2.rpar, correlation = FALSE)
summary(m2.mixed)##
## Call:
## mlogit(formula = RES ~ TIPOLOGIA + POSIZIONE + INQUILINI + SERVIZI +
## PREZZO | -1, data = data.mlogit, rpar = m2.rpar, correlation = FALSE,
## panel = TRUE)
##
## Frequencies of alternatives:choice
## first second third
## 0.34429 0.32081 0.33490
##
## bfgs method
## 23 iterations, 0h:0m:7s
## g'(-H)^-1g = 7.12E-07
## gradient close to zero
##
## Coefficients :
## Estimate Std. Error z-value Pr(>|z|)
## TIPOLOGIAsingola 2.55874151 0.23551443 10.8645 < 2.2e-16 ***
## POSIZIONE500m - 1.5km -0.27994808 0.16487619 -1.6979 0.089521 .
## POSIZIONE> 1.5km -1.64244110 0.17946007 -9.1521 < 2.2e-16 ***
## INQUILINI3-4 -0.24771233 0.13124913 -1.8873 0.059114 .
## INQUILINI5-6 -1.53129378 0.18167946 -8.4285 < 2.2e-16 ***
## SERVIZIlav. mic. -0.19916419 0.14338615 -1.3890 0.164831
## SERVIZIbalconcino -0.68726278 0.16587131 -4.1433 3.423e-05 ***
## PREZZO350 -0.80022315 0.12757799 -6.2724 3.555e-10 ***
## PREZZO450 -2.54714387 0.22207458 -11.4698 < 2.2e-16 ***
## sd.TIPOLOGIAsingola 1.88133558 0.24516100 7.6739 1.665e-14 ***
## sd.POSIZIONE500m - 1.5km -0.00057661 0.23306601 -0.0025 0.998026
## sd.POSIZIONE> 1.5km -0.74067211 0.22237162 -3.3308 0.000866 ***
## sd.INQUILINI3-4 1.04909143 0.18895054 5.5522 2.821e-08 ***
## sd.INQUILINI5-6 1.62062670 0.26326852 6.1558 7.470e-10 ***
## sd.SERVIZIlav. mic. 1.16694420 0.18899651 6.1744 6.641e-10 ***
## sd.SERVIZIbalconcino -0.23814246 0.21826260 -1.0911 0.275237
## sd.PREZZO350 0.29981682 0.19566567 1.5323 0.125451
## sd.PREZZO450 1.67484492 0.26862331 6.2349 4.520e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Log-Likelihood: -898.38
##
## random coefficients
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## TIPOLOGIAsingola -Inf 1.2897999 2.5587415 2.5587415 3.8276831 Inf
## POSIZIONE500m - 1.5km -Inf -0.2803370 -0.2799481 -0.2799481 -0.2795592 Inf
## POSIZIONE> 1.5km -Inf -2.1420168 -1.6424411 -1.6424411 -1.1428653 Inf
## INQUILINI3-4 -Inf -0.9553137 -0.2477123 -0.2477123 0.4598891 Inf
## INQUILINI5-6 -Inf -2.6243899 -1.5312938 -1.5312938 -0.4381977 Inf
## SERVIZIlav. mic. -Inf -0.9862561 -0.1991642 -0.1991642 0.5879277 Inf
## SERVIZIbalconcino -Inf -0.8478874 -0.6872628 -0.6872628 -0.5266381 Inf
## PREZZO350 -Inf -1.0024465 -0.8002232 -0.8002232 -0.5979998 Inf
## PREZZO450 -Inf -3.6768096 -2.5471439 -2.5471439 -1.4174781 Inf
Let’s first perform a likelihood ratio test in order to compare its performance with the previous model.
lrtest(m2, m2.mixed)## Likelihood ratio test
##
## Model 1: RES ~ TIPOLOGIA + POSIZIONE + INQUILINI + SERVIZI + PREZZO |
## -1
## Model 2: RES ~ TIPOLOGIA + POSIZIONE + INQUILINI + SERVIZI + PREZZO |
## -1
## #Df LogLik Df Chisq Pr(>Chisq)
## 1 9 -972.99
## 2 18 -898.38 9 149.23 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Looking at the test between the models m2 and m2.mixed, it can be seen that the p-value is very low, which implies that we have evidence to reject the null hypothesis that the variances of the random effects are all jointly equal to zero. Therefore, the random effects are significant in explaining consumer preferences and the m2.mixed model better fits with respect to the m2 model.
Now, looking at the output of the m2.mixed model, it can be seen that some variables have an high standard deviation, which means high heterogeneity. In particular, these variables are: TIPOLOGIAsingola, INQUILINI3-4, INQUILINI5-6, SERVIZIlav. mic. and PREZZO450. Considering the absolute values of these variables, it can be seen that for TIPOLOGIAsingola and PREZZO450 the heterogeneity is significant, but not relevant/strong (estimates are higher than standard deviations). On the other hand, all the other variables mentioned before show a relevant heterogeneity (standard deviations are significantly higher than the estimates).
Moreover, it is interesting to check if there is a change of sign in the random coefficients, which represent the distribution in quantiles. For example, in the case of TIPOLOGIAsingola, all values are positive, which means that there is substantial homogeneity in customer preferences, preferring the single room. Another example is the distance, POSIZIONE> 1.5km, with all negative values, which means that there is homogeneity, but students substantially prefer a distance ‘< 500m’. On the other hand, it can be seen that there is a change of sign in the variables INQUILINI3-4 and SERVIZIlav. mic., meaning that there is heterogeneity in customer preferences according to these two levels of attributes.
This can be visually seen by plotting the distributions:
par(mfrow=c(3,2))
par(mar=c(2,3,2,2))
plot(rpar(m2.mixed, "TIPOLOGIAsingola"))
plot(rpar(m2.mixed, "POSIZIONE500m - 1.5km"))
plot(rpar(m2.mixed, "POSIZIONE> 1.5km"))
plot(rpar(m2.mixed, "INQUILINI3-4"))
plot(rpar(m2.mixed, "INQUILINI5-6"))
plot(rpar(m2.mixed, "SERVIZIlav. mic."))
plot(rpar(m2.mixed, "SERVIZIbalconcino"))
plot(rpar(m2.mixed, "PREZZO350"))
plot(rpar(m2.mixed, "PREZZO450"))
As described before, heterogeneity in customer preferences is confirmed for the variables INQUILINI3-4 and SERVIZIlav. mic... Moreover, also INQUILINI5-6 shows a certain amount of heterogeneity (however less than a quantile). In addition, we can say that there could be a market niche for the variable INQUILINI5-6, with the 17% of customers who whould like to live with other 4/5 flatmates.
Moreover, it can be seen that all the values in the plot about the position are negative. It means that all students prefer to live near the university.
Concerning price, it can be seen that there could be another market niche in the distribution of PREZZO450, with 6% of students who can afford a room that costs 450 euros.
Another way to assess respondent heterogeneity is by looking at the
relationships between individual part worths (extracted with fitted())
and individual level variables.
# extract part woths
PW.ind <- fitted(m2.mixed, type = "parameters")
names(PW.ind)[1] <- "ID"
# heterogeneity wrt degree
degree.data <- unique(dataset[,c(1, 13)])
PW.degree <- merge(PW.ind, degree.data, by="ID")
# heterogeneity wrt sex
sex.data <- unique(dataset[dataset$SESSO != "Altro", c(1, 10)])
PW.sex <- merge(PW.ind, sex.data, by="ID")
# heterogeneity wrt distance from the university (fuori sede/pendolare)
dist.data <- unique(dataset[,c(1, 12)])
PW.dist <- merge(PW.ind, dist.data, by="ID")Let’s first analyze the relationship between the room’s typology and the degree attended by students.
boxplot(TIPOLOGIAsingola ~ LAUREA, data=PW.degree)
# by(PW.degree$TIPOLOGIAsingola, PW.degree$LAUREA, mean)
t.test(TIPOLOGIAsingola ~ LAUREA, data=PW.degree)##
## Welch Two Sample t-test
##
## data: TIPOLOGIAsingola by LAUREA
## t = 3.6237, df = 125.34, p-value = 0.0004205
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 0.3769906 1.2842843
## sample estimates:
## mean in group magistrale mean in group triennale
## 3.132188 2.301551
The boxplots show that both Master’s and Bachelor’s students prefer single rooms. Bachelor’s students’ data are more spreaded, in fact, even if the vast majority prefer a single room, there’s also someone who, on the one hand, tends to choose a double room and on the other hand, someone else who strongly prefers the single one. Furthermore, as we can see from the plot and from the t-test, we have evidence that Master’s students preferences towards the single room is higher than Bachelor’s ones.
The second relationship we are going to analyze is between sex and services. Concerning sex, since the category “Altro” counts only one respondent we are only comparing “F” and “M”.
boxplot(SERVIZIlav..mic. ~ SESSO, data=PW.sex)
# by(PW.sex$SERVIZIlav..mic., PW.sex$SESSO, mean)
t.test(SERVIZIlav..mic. ~ SESSO, data=PW.sex)##
## Welch Two Sample t-test
##
## data: SERVIZIlav..mic. by SESSO
## t = 1.3806, df = 79.998, p-value = 0.1712
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -0.08332799 0.46087711
## sample estimates:
## mean in group F mean in group M
## -0.1320484 -0.3208230
Once again we have homogeneity in the preferences between the considered categories of students. Both males and females prefer a living room rather than a dishwasher and a microwave. The difference between males and females is really low and not statistically significant.
Finally, we want to assess the relationship between the number of tenants and if students live in the city where they study or they reach it with means of transport (pendolare/fuori sede).
boxplot(INQUILINI3.4 ~ FUORISEDE_PENDOLARE, data=PW.dist)
# by(PW.dist$INQUILINI3.4, PW.dist$FUORISEDE_PENDOLARE, mean)Even in this case, all students agree and they prefer an apartment for 2 students instead of 3-4. We hypothesized that especially students who live in the city where they study but reside more than 300km away from it, could prefer a higher number of flatmates. In fact, we thought that since they do not have the possibility to come back home often, they are usually looking for more relationships with other students in the city. However, the data we have seem to falsify this hypothesis.
The results of our analysis allow us to answer the initial research questions.
-
Which room’s features are considered the most important by students? Which attributes’ levels are associated with a positive part worth?
According to the Multinomial Logit model, our sample of students consider the room’s typology, its position and its price as the most important features driving their choice. In particular, the room should be single, less than 500m away from the university and it should have a low price (250 euros). Other features associated with the most positive part worths are: 2 tenants and the living room. -
How can we assess the preference of a specific product profile we want to launch on the market? How can we increase its success?
We have considered Marta’s room as our reference product profile of which we want to assess students’ preference in comparison with other 7 competitors’ product profiles. By computing the preference share and by plotting the sensitivity chart, we gained useful information. Students appear to prefer Marta’s room instead of the competitors’ ones. We saw that in order to further increase the room’s success, we should evaluate if buying a dishwasher and a microwave is a sustainable choice. -
Are students’ preferences homogeneous towards the choice of the room?
The Multinomial Logit Model with random coefficients suggests that there is a certain amount of heterogeneity in students’ preferences. Concerning the room’s typology, its position and its price there is homogeneity: almost everyone prefers a single room, close to the university, characterized by a low price (only a really small portion of students can afford a 450 euros room). Looking instead at the number of tenants and at the services, respondents’ preferences appear to be polarized: the majority of students prefer an apartment with 2 tenants instead of 3-4 or 5-6, and a living room instead of a private balcony or a dishwasher and a microwave. However, there’s also a consistent portion of respondents who would choose 3-4 tenants instead of 2 and a dishwasher plus microwave instead of a living room. Furthermore, we can identify a possible market niche made of students who are willing to share the apartment with other 4-5 flatmates (5-6 tenants).
Finally, with respect to the individual level predictors we have considered, it resulted that students’ preferences were homogeneous towards a specific level of a specific attribute. The most significant result was that Master’s students’ show stronger preferences than Bachelor’s ones towards the single room.
In conclusion, from a managerial point of view we have found out that Marta’s room is meeting the tastes of students quite well. Moreover, in general we found evidence that it is easier to rent a single room, near the university, in an apartment with no more than 4 tenants, at less than 450 euros. Concerning the services, the dishwasher plus microwave and the living room are the most popular choices. Since the living room could be expensive because it is an additional empty room, the landlord could decide to rent it as a single room and to buy the dishwasher plus microwave for the apartment.