Jul 29, 2014 - Question-&-Answer (QA) websites have emerged as efficient platforms for knowledge sharing and problem solving. In particular, the Stack...

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arXiv:1407.5903v2 [cs.HC] 29 Jul 2014

Felipe Ortega DIS, University Rey Juan Carlos Mostoles, Spain. [email protected]

Gregorio Convertino Informatica Corporation Redwood City, CA, USA [email protected]

Massimo Zancanaro IRST, Fondazione Bruno Kessler Trento, Italy [email protected]

Tiziano Piccardi University of Trento Trento, Italy [email protected] true potential of knowledge sharing platforms that are powered by large-scale human participation. Traditional platforms for knowledge sharing and peer support such as mailing lists [13] have been eventually superseded by more interactive and dynamic environments such as forums, blogs and wikis [32]. Thus, a new area of big data analytics and application has emerged with the aim to understand and support such large-scale processes: see the growing number of studies on Wikipedia, Twitter, and social networking software tools.

ABSTRACT

Question-&-Answer (QA) websites have emerged as efficient platforms for knowledge sharing and problem solving. In particular, the Stack Exchange platform includes some of the most popular QA communities to date, such as Stack Overflow. Initial metrics used to assess the performance of these communities include summative statistics like the percentage of resolved questions or the average time to receive and validate correct answers. However, more advanced methods for longitudinal data analysis can provide further insights on the QA process, by enabling identification of key predictive factors and systematic comparison of performance across different QA communities. In this paper, we apply survival analysis to a selection of communities from the Stack Exchange platform. We illustrate the advantages of using the proposed methodology to characterize and evaluate the performance of QA communities, and then point to some implications for the design and management of QA platforms.

More recently, Question-&-Answer (QA) websites such as those comprising the Stack Exchange Network introduced new ways to improve the efficiency of problem-based sharing and collaboration in distributed communities. For instance, the inclusion of interesting gamification incentives [7] contributes to increase user engagement: respondents are granted a reputation score and a badge that reflect their speed to solve questions and the number of votes received by their answers. Some of these communities reached enough popularity to become the dominant platforms for worldwide knowledge exchange and problem solving in specialized domains [31]. Such is the case of StackOverflow, aimed at programmers, or Cross Validated, for people who must solve problems in statistics, machine learning, and data analytics. In fact, the former has been acclaimed as the ”fastest QA site in the West” in a previous research study [15], featuring more than 92% of its total number of questions answered in a median time of just 11 minutes.

Author Keywords

Question-and-Answer websites; Stack Exchange; Crowdsourcing; Performance Metrics; Survival Analysis. ACM Classification Keywords

H.3.4. Systems and Software: Performance evaluation (efficiency and effectiveness) General Terms

Design; Measurement; Performance.

Given these promising results, the utilization of QA platforms as a replacement of traditional help desk services in specialized domains increasingly appears a viable alternative. To test the feasibility of this alternative, it is essential that we can measure the performance of QA platforms using suitable data analytics methods. Stack Exchange regularly publishes detailed datasets tracking the question answering process in their 115 communities. Therefore this platform represents an excellent testbed to study the efficiency of QA platforms.

INTRODUCTION

Collaborative knowledge generation and problem solving have been transformed by social technologies over the past decade. The arrival of Web 2.0 technologies unleashed the Paste the appropriate copyright statement here. ACM now supports three different copyright statements: • ACM copyright: ACM holds the copyright on the work. This is the historical approach. • License: The author(s) retain copyright, but ACM receives an exclusive publication license. • Open Access: The author(s) wish to pay for the work to be open access. The additional fee must be paid to ACM. This text field is large enough to hold the appropriate release statement assuming it is single spaced.

Studies evaluating the performance of these communities have focused predominantly on descriptive metrics (e.g. mean/median answering time, proportion of solved questions, etc.), as in [15]. However, more advanced methods for lon1

tion from researchers as big data resources for studying community phenomena and design future technologies, as witnessed by the growing number of papers published each year on QA sites (e.g., http://meta.stackoverflow.com/q/134495).

gitudinal data analysis are required to integrate temporal information about the question resolution process as an integral part of the evaluation model. Survival analysis provides methodology and statistical techniques for the analysis of time-to-event data [11] that can fill the current methodological gap. In our application of this analysis, we define the event of interest as the ”time elapsed until a question is resolved”.

The studies have focused on a variety of facets of the QA communities. Several of the early investigations have focused on modeling expertise of users [35, 1]. But more recently there is growing interest for characterizing the principles that regulate the process of QA [2]. Some studies started analyzing the factors that may predict user intent [5]; the quality of the answer [33] and the likelihood of getting an answer [30]. In our own previous work, we have analyzed the impact of some non content-related characteristics of the question to estimate the likelihood that a given question will receive a satisfactory answer in a reasonable time [21]. In turn, Tausczik et al. try to predict the perceived quality of online mathematics contributions from users’ reputations [27, 28].

Survival analysis has already been applied in big data analytics for web systems, such as modeling conversions in online advertising [4]. The method can also incorporate valuable information about unresolved questions, which have been often been overlooked in prior studies. But, predicting unanswered questions is a critical goal of our work because we are testing the applicability of QA platforms for offering reliable customer support service in specialized domains: i.e., while having 8% of unanswered questions is acceptable for the StackOverflow site, the same would not be admissible for a company that sells this service to business customers.

Arguably the most complete report on StackOverflow up to 2011, [15] characterized the site’s properties and evolution that contributed to its success. Focusing on questions that eventually received answers, they reported a median time for first answers of 11 minutes and a median time for accepted answers of 21 minutes, which are consistent with our subsequent analysis [21].

Hence, the aim of this paper is to introduce the use of survival analysis to model the occurrence of events of interest in online communities and web systems through the analysis of big datasets. This will lead us to: • Characterize and compare the performance of different QA sites in which an event of interest occurs; • Identify relevant factors that exert a positive or negative influence over the happening of such event of interest; • Estimate the expected time of occurrence of future events of interest.

Although for some respect different, Yahoo! Answers is another commonly studied QA site. Differently from the Stack Exchange, this site is for general-purpose questions. It had 60 million unique visitors and 160 millions answers within the first year [20]. Between 2011 and 2012, it attracted between 17 and 24 million unique visitors per month. Yahoo! Answers has attracted a relevant number of studies too. In [5], Chen and colleagues classify questions in three categories according to their underlying user intent: subjective, objective, and social. They build a predictive model through machine learning based on both text and metadata features (topic, time, user expertise). Wang et al. [33] point to the problem of low-value questions introducing noise as sites grow: they report signs of stalling in the user growth of Yahoo! Answers, with traffic dropping 23% in a span of four months in 2011.

We analyze the performance as time to answer in eight different sites on the Stack Exchange platform. Through this study, we first illustrate the applicability of survival analysis for big data analytics and then draw implications for the design and management of QA platforms. RELATED RESEARCH

QA sites are a Web 2.0 technology increasingly adopted by self-help communities of experts such as programmers, mathematicians, and statisticians. As a result, these sites are changing the ways in which these communities share knowledge and collaborate on problem solving. For example, Vasilescu and collaborators found in [31] that the emergence of a QA community in Stack Exchange is causing experts in a specific community to migrate from an existing mailing list (r-help) to a Stack Exchange site (as part of StackOverflow), where their behaviour is different. The migration appears motivated by the incentives and gamification mechanisms applied in Stack Exchange to engage the users. Tausczik et al. [26] present qualitative findings on the uses of MathOverflow by mathematicians as a large-scale problem-solving platform. While there is evidence of new emerging practices, however, most of the studies have focused on individual QA communities, which limits generalizability, and contributed findings that are often anecdotal or descriptive rather than predictive in nature.

METHODOLOGY AND DEFINITIONS

In this section, we first describe the public data sources that we have used. Then, we introduce the essential elements of survival analysis required to understand and interpret the results of the study. Finally, we introduce the features used in order to model the time to answer a question. Data sources: Stack Exchange Data Dumps

Every 3 months, Stack Exchange publishes anonymized dumps of all content stored in databases of their public QA sites (115 different communities, to date). The data is hosted by the Internet Archive project (https://archive. org/details/stackexchange) and it is available for direct download or using the BitTorrent file sharing protocol. The dump files include information in XML format (except for users’ account data) for each site in the platform, or network, and it can be used for research purposes.

Despite the current methodological limitations, QA sites (and Stack Exchange in particular) are receiving increasing atten2

troduce this and other details about survival analysis in the following subsection.

Data included in these dump files characterize question threads: comments, answers, answers marked as accepted, votes received by the answers, badges and special user levels granted to users based on their question-solving merits, etc. The datasets that we analyzed were released in March 2013 and included the most up-to-date version of each question thread along with the history of each post (edits, votes, etc).

Survival Analysis

We introduce here a collection of statistical methods and techniques to handle timing and duration until a certain event of interest occurs. Although these techniques are frequently referred to as survival analysis in disciplines like medicine, biostatistics and epidemiology, they are also well-known in other scientific areas under different names [17]: reliability analysis (engineering and production); duration model (economics) and event history analysis (social sciences). In spite of this, these techniques are rarely applied in computer science. We could find only a few studies that applied survival analysis: e.g., to model the retention of contributors in open collaborative projects [19, 34], gender imbalance in Wikipedia [14] or the duration of open source projects [23].

We used a relational database (PostgreSQL) to rebuild the original data model and for computing new aggregate information. We created some intermediate tables for an incremental analysis during the features selection stage. In this phase, to select the most relevant features we generated descriptive statistics for each aspect of the communities using the R programming language. The list of relevant features considered will be described below. In particular, we have focused the scope of this analysis on a subset of eight communities in the Stack Exchange network, representing a variety of application domains:

The goal of survival analysis is to model the hazard rate, that is, the conditional probability that an event of interest occurs at a specific time interval t. Let T be a random variable representing the time until the event of interest happens which,in our case, will be ”time until a question is resolved” (measured in minutes). Thus, the hazard rate represents the rate at which questions in our study experiment this event at time t, conditional on surviving (not experiencing the event) up to that time:

• Apple (AskDifferent): Apple users and developers. • AskUbuntu: Ubuntu users and developers. • Math (Mathematics): Math students, instructors, and professionals in this field. • ServerFault: system and network administrators. • SharePoint: SharePoint users and developers. • StackOverflow: professional and enthusiast programmers. • SuperUser: computer enthusiasts and power users. • Wordpress (Wordpress Answers): Wordpress administrators and developers.

h(t) = lim

∆t→0

P r [(t ≤ T < t + ∆t) |T ≥ t] ∆t

(1)

Hence, in equation (1), h(t) represents the instantaneous risk that the event of interest happens in the interval [t, t + ∆t]. Along with the hazard rate, it is frequent to consider the survival function, S(t), which indicates the probability that the survival time T is greater or equal than a given time t. Both functions are related in the following way:

To undertake this study, we took a random sample of 5,000 questions from each site. In each sample, we filtered out all cases of questions showing obvious wrong values for the resolution datetime field (for instance, lower than the creation datetime). These values were due to spurious inconsistencies in the creation of dump files. Questions can receive several answers and site users can cast votes on these answers to help indicate which are, in their opinion, the most useful ones. However, only the original user who posted a question can finally mark it as resolved, by picking up one of the answers as accepted. This may or may not coincide with the answer that received the highest number of votes. Therefore, the voting process provides an alternative metric to assess the respondents’ reputation level. Questions marked as off-topic and removed by site moderators have been filtered out of our analysis.

h(t) =

f (t) S(t)

(2)

Where f (t) is the unconditional probability density function of the random variable T , representing survival time. For descriptive purposes, a non-parametric method known as the Kaplan-Meier (KM) estimator [12] is usually applied to obtain a graphical representation of the survival function. A remarkable feature of survival analysis is that it can accommodate censored data. In the most frequent cases, either the observation period expires or a subject is removed from the study before the event of interest occurs. In these cases, we have some information about survival time, but not the exact value of that survival time. All we know is that the event of interest did not occur (yet) by the end of the study. This is called right-censoring and it is the only form of censoring accounted for in this analysis. Thus, right-censored cases correspond to questions that either not received any answer or, despite receiving any answer, it has not been accepted by the author of the question.

In our case, we are interested in modeling the time elapsed until each question is resolved in the eight communities included in the study. To this aim, we created a dummy variable status to identify answers that were marked as accepted from those still waiting for resolution (even if they may have already received answers). Then, we apply survival analysis to create a model for the time elapsed until questions are resolved, using this binary indicator to identify our event of interest. A key advantage of survival analysis is that it can also include information about unresolved questions (censored) in the model, which leads to more accurate estimations. We in3

This offers a key advantage for the study of time-to-event data (Hosmer, 2007), as we are not forced to make any assumptions about the status of questions that could be eventually resolved in the future, after the end of the observation period. As a result, predictions about the expected resolution time for new questions are likely to be less biased.

Moreover, additional functions included in the rms package let users represent the effects of covariates graphically taking these transformations into account, so that results are plotted back on the original scale of the model’s covariates to facilitate their intuitive interpretation. In the same way, multilevel confidence intervals can be computed to visually assess the size of effects of independent parameters on the log hazard ratio, according to modern strategies for informative and robust evaluation of statistical models [6]. We will make use of these features to present the results of our survival model fitting on the Stack Exchange sites under study in the following sections.

One of the most popular models in survival analysis is the Cox proportional-hazards model (Cox PH). In this model, the hazard rate is represented by:

hi (t) = h0 (t) exp (β1 xi1 + β2 xi2 + · · · + βk xik )

(3) Relevant features to model question answering

Table 1 summarizes the list of features that we include as covariates to model the resolution time of questions in the eight communities analyzed with the the Cox PH model.

Where h0 (t) represents a baseline hazard function that remains unspecified, xik are k fixed covariates for each observation i, and βk are k regression coefficients. The model is usually expressed in terms of the hazard ratio of two given observations, i and j: log

hi (t) hj (t)

Feature

Type

Description

bodylength

Integer

titlelength

Integer

hasexample

Boolean

tagscount

Integer

sumpeople

Integer

zscore

Decimal

Number of printable characters in the body of questions (HTML filtered out). Number of printable characters in the title of questions (HTML filtered out). Dummy variable, indicates if the question contains an example (e.g. code). Number of tags used in the question, for content classification (values in [2, 5]). The sum of the sizes of the tag-based communities of respondents, considering all the tags of the question. We compute in advance the number of active contributors for each tag. Normalized ratio of the difference between questions and answers posted. That is, answering a greater proportion of questions (relative to one’s own activity) implies higher expertise.

= β1 xi1 + β2 xi2 + · · · + βk xik

(4)

Similarly to the log-odds ratio in logistic regression models, the hazard ratio is easy to interpret in this case, since the baseline hazard function h0 (t) cancels out in the numerator and denominator of equation 4. Therefore, the hazard ratio between any two observations is independent of time. This is why the Cox model is called a proportional hazards model. We use it to identify any covariates that influence (in a positive or negative way) the resolution time of questions. Once the model is specified, we can obtain an estimation of the influence of each covariate on the hazard function. Likewise, we can also predict the expected survival time for new cases. In spite of these advantages, this standard formulation of the Cox PH model assumes that all covariates enter the model in a linear fashion. However, it is quite frequent that the log hazard ration (output variable) does not depend linearly on some of the model’s covariates. In this case, it is necessary to relax the linearity assumptions for model parameters, as explained in section 2.4 of [10]. A practical alternative to achieve this goal is using the so-called restricted cubic splines functions with k knots, introduced by Stone and Koo in [24], to transform any covariates we may suspect that do not follow a linear relationship with the outcome variable. The library rms for the R statistical programming language [22] implements many advanced techniques explained in [10] and provides support for this transformation on independent parameters with the rcs() function (along with other possible alternatives). For an independent parameter X in the model, the restricted cubic spline function with k knots t1 , . . . , tk is given by [8]:

Table 1: List of relevant features to be included in the survival model for time to answer questions. These six features have been included in our model based on theoretical background supporting their relationship with the question answering process.

f (X) = β0 + β1X + β2(X − t1 )3 + β3 (X − t2 )3 + + . . . + βk+1 (X − tk )3 (5) 4

The body length is the number of printable characters in the body of the question after filtering out the HTML formatting. It is considered important since unanswered questions are sometimes too short [30] or, on the contrary, they may be too long and tedious [15]. The title length is the number of printable characters in the title. Treude and colleagues [30] discussed the importance of the title in at least one QA site in attracting the attention of the community. We consider the length of a title as a proxy of its content.

Now, we present the results of a descriptive analysis of the time to answer questions, using the Kaplan-Meier nonparametric estimator. Figure 1 depicts the estimated survival function S(t) for each site. As we introduced above, this function is directly linked to the hazard rate. It indicates the absolute probability that a survival time T is greater or equal than some time t [17]. Therefore, this function represents the proportion of subjects surviving beyond time t, and at t = 0, S(0) = 1. In our study, the curve for each site represents the proportion of questions that remained unsolved for T ≥ t.

Has example is a Boolean variable that indicates whether the question includes an example (for instance, a snippet of programming code). The importance of examples have been discussed by several previous studies [3, 15, 30].

1.0

S(t) time to answer in StackExchange

0.4

S(t)

0.6

0.8

Tagscount is the number of tags used in the question. Although this aspect has not been directly discussed in literature, there is some evidence supporting that if questioners facilitate a quick understanding of the main topic(s) in the content of questions this may increase the likelihood of getting answers [30, 3]. StackOverflow’s guidelines encourage the use of tags (up to 5) exactly to meet this purpose.

0.0

0.2

Sum people is a measure of how many persons will be exposed to the questions. As discussed by Harper and colleagues [9] a wider audience increases the likelihood for a question to be answered. In the same way, open collaborative projects are known to benefit from a large a varied audience (in terms of previous background and expertise) to solve specific problems, following the wisdom of crowds effect explained by Surowiecki [25].

0

500000

1000000

1500000

2000000

minutes

Figure 1: Non-parametric Kaplan-Meier estimators of survival functions for time to answer questions in 8 communities from the Stack Exchange network

Finally, the zscore metric has been introduced by Zhang and colleagues in their analysis of the Java Forum [35]. It is computed as the normalized ratio of the difference between questions and answers and it models the understanding that answering a greater proportion of questions (relative to one’s own activity) implies higher expertise. Hence, this feature is calculated as follows: |a| − |q| zscore = p , |a| + |q|

apple askubuntu math serverfault sharepoint stackoverflow superuser wordpress

Visual inspection suggests common patterns but also performance differences among the eight communities under study. In all cases, the proportion of questions that remain unsolved quickly drops below 40%, showing a good performance on question resolution for all sites. However, the main differences among sites emerge from their efficiency dealing with questions that remain unsolved for longer periods of time. For instance, these correspond to questions that may be harder to solve (for some reason) or that do not attract enough attention from the respondents audience.

(6)

where a is the number of answers and q is the number of questions posted by the user. Since this value changes in time, for each question we used the posts history to compute the zscore of the author at the posting time. For each question and answer, we assigned an incremental counter to keep track of their temporal position.

Listing 1 presents the descriptive summary for each site, created with the survival package in the R programming language [29]. We can see the total number of questions in each sample (after removing obvious erroneous cases), the median survival time and 95% confidence intervals for this median value.

RESULTS

> stackex_surv = with(survdata, Surv(tanswer, solved)) > stackex_fit = with(survdata, survfit(stackex_surv ˜ site )) > print(stackex_fit) Call: survfit.formula(formula = stackex_surv ˜ site)

In this section, we lay out the main results of our study. In the first place, we evaluate the performance of the different sites regarding the time to solve questions comparing the estimators of their corresponding survival functions. This is followed by the results of fitting a Cox PH model for each site, using the 6 relevant covariates presented above whose role is supported by previous research in this area.

apple askubuntu math serverfault sharepoint stackoverflow

Comparing the performance of QA communities

5

records events median 0.95LCL 0.95UCL 4296 3416 210.0 186.0 247.3 3983 2759 904.4 607.1 1208.9 4744 3999 39.6 35.9 43.2 4552 3702 84.6 73.8 96.2 4335 3137 417.7 343.3 505.0 4779 3844 35.8 31.9 42.6

superuser wordpress

4467 4187

3433 3617

100.8 109.5

87.9 97.9

This approach obtained much better diagnostics than a single model for all sites. Of particular importance is testing the validity of the proportional hazards assumption, which can be checked through plots of the scaled Schoenfeld residuals for each parameter against time [17]. If this assumption holds, the plots must not show any pattern for residuals over time. In addition, an individual test is computed to evaluate evidence of a non-null correlation coefficient of these residuals over time. Listing 3 presents the results of this test for the apple community, obtained with the cox.zph function in the survival library for R. We confirm that there is no strong evidence to discard the null hypothesis of a correlation coefficient rho = 0 for any parameter in the model with time. Similar successful diagnostics were obtained for all remaining Cox PH models in this analysis.

116.3 120.4

Listing 1: Summary of number of events (solved questions), median survival time (in minutes) and its associated 95% confidence interval for each site. In particular, the median survival time at which 50% of all questions in each sample are resolved is estimated by tracing an horizontal line at 0.5 on the plot of the survival curve. Both solved questions (with an accepted answer) and unresolved ones (right-censored cases) are included in the nonparametric estimation of the survival curve. As we can see, the performance on question resolution is quite different in each site. While StackOverflow or Math present low median survival times of slightly more than 30 minutes, AskUbuntu needs more than 15 hours (904.4 minutes) to resolve half of the total number of questions in the sample.

zscore bodylength titlelength hasexample tagscount sumpeople GLOBAL

A Mantel-Haenszel test [16] to formally check for statistically significant differences of survival curves among sites returned a Chi-square value of 1084 on 7 degrees of freedom, with a virtually null p-value. Hence, we can conclude that there exist significant differences in the ability of different sites in the study to resolve questions.

rho -0.00777 -0.01705 0.00687 -0.02363 -0.01767 0.00639 NA

chisq 0.170 0.999 0.162 1.944 1.069 0.138 6.779

p 0.680 0.318 0.687 0.163 0.301 0.711 0.342

Listing 3: Model formulation to fit a Cox PH model for each site using the cph function in the rms package in R.

Modeling question answering processes

As we introduced above, the Cox proportional hazards model (Cox PH) let us create survival models for inference and prediction of hazard rates, without forcing us to choose a predefined parametric form of the baseline hazard function. In this study, we use the six features presented above as parameters of our Cox PH model.

Table 2 summarizes multilevel estimations (combining contributions from linear and non-linear components) of the hazard ratio for each covariate considered in our model. For continuous parameters, the hazard ratio is calculated between the upper and lower values of the inter-quartile range, controlling for all other covariates. For the categorical parameter hasexample, it is computed between the two possible categories, again controlling for all other covariates.

We first transform the continuous parameters bodylength, titlelength and sumpeople by taking the natural logarithm (log) to reduced initial skewness in their distribution of values. Then, we apply a restricted cubic spline with 3 knots (rcs(x, 3)) to all parameters except for hasexample (a binary categorical parameter) and tagscount (restricted to the interval [2, 5]), as we suspect that all other covariates may not follow a strictly linear relationship with the log hazard ratio.

Interpreting the statistical significance of each covariate on the hazard ratio can be misleading if we base our considerations solely on traditional significance tests for individual model coefficients and the associated p-values. In situations like this, where we have both linear and non-linear components (from the restricted cubic splines transformation), it is non-trivial to interpret p-values calculated for each individual component. Furthermore, p-values can be misleading with large√samples, as the test statistic is inversely proportional to the n, being n the size of the sample. Since we used large samples (n ∼ 5, 000), it becomes harder to know if what we are observing are true effects or just noise.

We use the cph function included in the rms package of the R statistical language to fit a Cox PH model with the formulation presented in Listing 2. Initially, we attempted to fit a single model to all data sampled from the eight sites under study, introducing an additional multilevel categorical parameter to identify the effect of each site. However, model results and diagnostics showed a very poor fit. This suggested the alternative of fitting an individual Cox PH model for each site, as not all independent parameters may exert the same influence for all sites.

To avoid these issues, we preferred to report multilevel confidence intervals (adjusted to combine linear and non-linear components in our model). By doing so, we follow modern approaches in reporting and assessment of statistical models [6]. Figure 2 shows such a plot, created with the rms package in R. For each point estimator of the hazard ratio (marked with a red triangle) confidence intervals are plotted at levels 0.9, 0.95 and 0.99. The vertical dashed line marks the unity value for the hazard ratio (no effect). In consequence, if the confidence intervals include the dashed line we do not have strong empirical evidence of a significant effect for the corresponding covariate. Otherwise, there is strong evidence

> cph(formula = Surv(tanswer, solved) ˜ rcs(zscore, 3) + rcs(log(bodylength), 3) + rcs(log(titlelength), 3) + hasexample + tagscount + rcs(log(sumpeople), 3), data = data_stackow, method = "efron", x=T, y=T, surv=T)

Listing 2: Model formulation to fit a Cox PH model for each site using the cph function in the rms package in R.

6

0.75

0.80

0.85

Hazard Ratio 0.90 0.95 1.00

1.05

1.15

0.75

zscore − 37.34:36.32

zscore − 37.34:36.44

bodylength − 521:206

bodylength − 600:213

titlelength − 68:41

titlelength − 61:36

tagscount − 3:2

tagscount − 3:2

sumpeople − 2184:531

sumpeople − 3565:676

hasexample − true:false

0.85

Hazard Ratio 0.95 1.05

1.15

1.25

1.35

hasexample − true:false

(a) Apple

0.60

0.70

0.80

Hazard Ratio 0.90 1.00

(b) AskUbuntu

1.20

1.40

1.60

0.80

zscore − 37.34:34.81

zscore − 37.34:36.07

bodylength − 655:227

bodylength − 848:298

titlelength − 66:35

titlelength − 63:37

tagscount − 3:1

tagscount − 4:2

sumpeople − 2313:784

sumpeople − 6020:1341

hasexample − true:false

hasexample − true:false

(c) Math

0.80

Hazard Ratio 0.95 1.05

0.85

1.15

1.25

1.35

0.70 zscore − 37.34:34.65

bodylength − 748:256

bodylength − 978:306

titlelength − 66:40

titlelength − 63:37

tagscount − 3:2

tagscount − 4:2

sumpeople − 906:230

sumpeople − 104060:25439

hasexample − true:false

hasexample − false:true

(e) SharePoint

0.80

0.85

Hazard Ratio 0.90 0.95 1.00

1.20

1.30

1.40

0.80

Hazard Ratio 0.90 1.00

1.20

1.40

1.60

(f) StackOverflow

1.10

1.20

0.80

zscore − 37.34:36.07

zscore − 37.34:35.79

bodylength − 591:223

bodylength − 825:279

titlelength − 65:39

titlelength − 61:37

tagscount − 4:2

tagscount − 3:2

sumpeople − 10608:1576

sumpeople − 1078:335

hasexample − true:false

hasexample − false:true

(g) Superuser

Hazard Ratio 1.00 1.10

(d) ServerFault

zscore − 37.34:35.34

0.75

0.90

0.85

Hazard Ratio 0.90 0.95 1.00

1.05

1.10

(h) Wordpress

Figure 2: Estimated hazard ratios and multilevel confidence intervals at 90% (dark blue), 95% (blue) and 99% (light blue) for model covariates in each site. Hazard ratios are calculated between the lower and upper limits of the interquartile range (continuous variables) or comparing between levels (categorical variables), as indicated next to the label of each covariate. 7

zscore bodylength titlelength tagscount sumpeople hasexample

Apple

AskUbuntu

Math

ServerFault

SharePoint

StackOverflow

SuperUser

Wordpress

0.96 0.79 0.94 0.95 1.09 0.98

0.92 0.76 1.04 1.01 0.98 1.22

0.97 0.77 1.04 0.64 1.44 0.94

0.95 0.80 0.96 0.89 1.28 0.96

0.98 0.81 0.93 0.94 1.09 1.19

0.98 0.74 0.94 0.83 1.46 0.70

0.97 0.77 0.98 0.94 1.08 1.06

0.96 0.80 0.94 0.94 1.07 0.89

Table 2: Estimators of the hazard ratio corresponding to each covariate considered in the Cox PH model. Green colours indicate positive effects (increasing hazard ratio), whereas red colours mark negative effects (decreasing hazard ratio). supporting the claim for such an effect of that covariate on the hazard ratio.

which holds in the context of the features that we have selected (see also further discussion in the conclusion section), suggests a few implications for the design of QA platforms.

Finally, in addition to the point estimators for effects on the hazard ratio presented above, it is also possible to create effect plots showing the influence of each covariate along a range of values, controlling for all other covariates. This is also a very useful feature shipped in the rms package in R. Figure 3 show these plots for each covariate in our model in the case of the stackoverflow site. Besides, these graphs are already adjusted to plot the effects on the original scale of each covariate in the model, as the package can ’remember’ the transformations that were applied to each parameter. 95% confidence intervals are also presented in shaded grey along each effect curve.

In the first place, to best predict question resolution site by site, software platforms that support multiple QA sites (and involving humans via mixed-initiative user interfaces) should surface unique subsets of predictive features within the automatic predictor (i.e., to inform the human) and the user interface (i.e., to guide the human as s/he acts on the question) (e.g., see [21]). Moreover, even when two QA sites share the same set of predictive feature, the underlying QA software platform should accommodate unique prioritization of the subsets of features within the automatic predictor and the user interface: i.e., two different QA sites running on the same platform with the same set of predicting features may surface them with different priorities; the same site that changes significantly over time may surface the features with different priorities along its lifecycle.

This type of graph allows to visually interpret the shape of effects on the outcome variable. For example we can see that the strong effect reported for the bodylength parameter presents a smoothed declining shape. For very short values of bodylength (short questions) the log hazard ratio increases and thus the chances of a question to be resolved. However, questions with bodylength values greater than 1 KB have a negative log hazard ratio, indicating a lower chance of being resolved. Likewise, we can confirm that questions including an example increase their chances to be resolved, but those without an example decrease their likelihood of being resolved. Finally, we need more than 50,000 users subscribed to the tags used to label the question to increase it chance of being resolved, and this effect grows rapidly as the size of the audience increases. This provides empirical evidence for a wisdom of the crowd effect [25] in StackOverflow: the larger the audience, the higher the chance of resolving our question.

The second implication for design may even bring us to a more ambitious vision to move from systems that are first designed, then used, and eventually redesigned, to systems that allow for QA site use and adaptive redesign to run in parallel as the underlying QA platform detects from the site usage history what are its current subset of predictors (significant estimators) and model coefficients (size of effects per estimator). Indeed, a limitation seldom discussed of accurate modelling of services is the case when they are used to improve the service, whose technology infrastructure might become outdated by the time is design, tested, and deployed.

CONCLUSIONS AND FUTURE WORK IMPLICATIONS FOR TOOL DESIGN AND MANAGEMENT

In this paper, we have used survival analysis to model the time to answer questions posed on a wide set of different QA sites taken from the same QA platform. Since the test for PH assumption holds in our analysis, survival models are valid and can be used to predict the speed to answer questions in a QA site that is comparable to those we analyzed.

Since a survival model built along the lines discussed above may indicate the likelihood of a given question to receive an answer and provide a reasonable estimation of the time it will take, these aspects may be used to improve QA platforms in different ways: by either providing an automatic feedback to the questioner or, as in the hybrid design proposed in our previous work [21], to merge crowdsourcing with an expertbased model to improve the efficacy of the service.

We explicitly decided not include content-based analysis in order to improve portability of the models across different QA domains (e.g. programming vs. Math). Of course, this is at the same time a limitation and an opportunity for future work since content-based features are likely to improve accuracy of models [18].

A first important lesson that emerges from the results is that a one-model-fits-all approach is less effective than a sitespecific approach in building predictive models. This lesson, 8

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Figure 3: Plots of effects of covariates included in the model on the log hazard ratio for the stackoverflow site. Furthermore, we have driven our feature set from a literature survey and there is no direct evidence that a different set of features cannot be more useful. Although this aspect may be part of our future work, we contend that our features are good enough for a baseline model and that they are easy to compute. Further work is definitely needed to provide generalized figures of merits.

unanswered questions of stack overflow. In Proceedings of the Tenth International Workshop on Mining Software Repositories, IEEE Press (2013), 97–100. 4. Chandler-Pepelnjak, J. Modeling Conversions in Online Advertising. PhD thesis, The University of Montana, 2010. 5. Chen, L., Zhang, D., and Mark, L. Understanding user intent in community question answering. In Proceedings of the 21st international conference companion on World Wide Web, ACM (2012), 823–828.

Overall, we believe that the present study shed some new light on the field of crowd-based QA sites and it provides a new approach through survival analysis to model one of the crucial aspects in this field, namely to determine the likelihood of a question to receive an answer and an estimation of the time required to receive the accepted answer that solves that question.

6. Cumming, G. Understanding the new statistics: Effect sizes, confidence intervals, and meta-analysis. Routledge, 2013. 7. Deterding, S., Dixon, D., Khaled, R., and Nacke, L. From game design elements to gamefulness: defining gamification. In Proceedings of the 15th International Academic MindTrek Conference: Envisioning Future Media Environments, ACM (2011), 9–15.

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