A Large-Scale Constrained Joint Modeling Approach for Predicting User Activity, Engagement, and Churn With Application to Freemium Mobile Games
Bibliographic record
Abstract
We develop a constrained extremely zero inflated joint (CEZIJ) modeling framework for simultaneously analyzing player activity, engagement, and dropouts (churns) in app-based mobile freemium games. Our proposed framework addresses the complex interdependencies between a player’s decision to use a freemium product, the extent of her direct and indirect engagement with the product and her decision to permanently drop its usage. CEZIJ extends the existing class of joint models for longitudinal and survival data in several ways. It not only accommodates extremely zero-inflated responses in a joint model setting but also incorporates domain-specific, convex structural constraints on the model parameters. Longitudinal data from app-based mobile games usually exhibit a large set of potential predictors and choosing the relevant set of predictors is highly desirable for various purposes including improved predictability. To achieve this goal, CEZIJ conducts simultaneous, coordinated selection of fixed and random effects in high-dimensional penalized generalized linear mixed models. For analyzing such large-scale datasets, variable selection and estimation are conducted via a distributed computing based split-and-conquer approach that massively increases scalability and provides better predictive performance over competing predictive methods. Our results reveal codependencies between varied player characteristics that promote player activity and engagement. Furthermore, the predicted churn probabilities exhibit idiosyncratic clusters of player profiles over time based on which marketers and game managers can segment the playing population for improved monetization of app-based freemium games. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.009 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".