Panel Dynamic Logistic Regression

Customer Analytics Classification

Customers who bought last week are likelier to buy this week. Find out whether that is habit (buying makes them buy again) or loyalty (some customers were always going to buy), because the two call for opposite marketing.

QUICK START: Choose Your Path

OVERVIEW & WHAT THIS TOOL SOLVES

A brand manager wants to mail 20,000 "first bottle free" coupons ($70,000) because loyalty-card data shows a shopper who bought last week is far likelier to buy this week. A free trial that turns a shopper into a regular (True Habit) pays for itself many times over; one that goes to someone who was going to buy anyway (Baseline Loyalty) is $3.50 handed away. This tool estimates three nested panel models to pull true habit apart from pre-existing customer loyalty.

🎯 Questions It Answers

Does buying this week actually cause a shopper to come back next week (habit), or are we just seeing loyal fans repeat-buy?
Will a "first purchase free" trial coupon echo into extra future orders after the promotion ends?
How much is our promotional lift inflated because offers were targeted to our best customers?

📂 What Data You Need

A balanced or unbalanced customer panel (one row per customer per period, e.g., week or month).
Customer ID, Period Index, and a binary 0/1 Outcome (bought, renewed, opened app).
Optional time-varying drivers (coupon, feature, price) and a static customer segment column.

💡 What You'll Discover

Side-by-Side Model Ladder (A, B, C): Watch how pooled habit shrinks once customer heterogeneity is accounted for.
Trial Echo Multiplier: Extra future purchases generated per induced trial order.
Out-of-Sample Holdout Check: Forecast accuracy on held-back future periods vs. each customer's own baseline rate.

🔍 Key Nuances & Common Traps to Watch For Click to expand ▾

"Bought last week" has two explanations that need opposite marketing: True habit (state dependence) means trial subsidies pay back across future periods; loyalty (unobserved heterogeneity) means targeting existing fans pays back, while blanket trial coupons subsidize purchases that would have happened anyway.
Why a pooled model (Model A) always overstates habit: Stacking all customer-weeks together lets loyal regulars' long buying streaks pose as habit.
Why fixed effects fail on short panels (The Nickell Problem): Giving every customer a separate dummy intercept alongside a lagged outcome $y_{i,t-1}$ biases the habit estimate downward when panel history $T$ is short—which is why Model C uses correlated random effects (Wooldridge / Mundlak).

📐 Under the Hood: Model Equations & Variable Definitions Click to expand ▾

The Three-Model Ladder (Pooled → Mundlak/Wooldridge → Random Effects) Panel Dynamic Logit

\[ \text{Model A (Pooled):} \quad \operatorname{logit} P(y_{it}=1) = \alpha + \phi\, y_{i,t-1} + \beta x_{it} \] \[ \text{Model B (Observed History):} \quad \operatorname{logit} P(y_{it}=1) = \alpha + \phi\, y_{i,t-1} + \beta x_{it} + \gamma_0 y_{i0} + \gamma \bar{x}_i \] \[ \text{Model C (Random Effects):} \quad \operatorname{logit} P(y_{it}=1) = \alpha + \phi\, y_{i,t-1} + \beta x_{it} + \gamma_0 y_{i0} + \gamma \bar{x}_i + u_i, \quad u_i \sim \mathcal{N}(0, \sigma^2) \]

💬 Read it in plain English: Model A assumes all shoppers start with the same baseline appetite; Model B adjusts for each shopper's initial purchase and average exposure to promotions; Model C gives every shopper their own persistent latent loyalty baseline $u_i$ so that $\phi$ captures only true week-to-week habit.

Variable & Symbol Directory (Every Term Defined) Hover or focus any role badge for details

y_it, y_i,t-1

Current & Prior Period Purchase (0/1) YOUR DATA ⓘ

Equals $1$ if customer $i$ bought in period $t$ (or $t-1$), and $0$ otherwise.

True Habit (State Dependence) ESTIMATED ⓘ

How much buying in period $t-1$ causally shifts the log-odds of buying in period $t$.

β, x_it

Marketing Driver Slope & Value ESTIMATED ⓘ

$x_{it}$ is customer $i$'s promotional/marketing input in period $t$; $\beta$ is its immediate effect.

γ₀, y_i0

Initial-Condition Anchor (Wooldridge) ESTIMATED ⓘ

$y_{i0}$ is customer $i$'s period-0 purchase indicator; $\gamma_0$ absorbs pre-sample loyalty differences.

γ, x̄_i

Mundlak Customer-Mean Adjustment ESTIMATED ⓘ

$\bar{x}_i$ is customer $i$'s average driver exposure across all periods; $\gamma$ captures targeting correlation.

u_i, σ

Unobserved Customer Loyalty (Random Effect) ESTIMATED ⓘ

$u_i$ is customer $i$'s time-invariant latent loyalty; $\sigma$ measures how widely baseline loyalty varies across shoppers.

Step 1DATA SOURCE

Start with a case: each was generated from a known model (or, for Crave, comes from the CLV tool with its model known), so at the end you can check the three models against the truth. Or bring your own panel: one row per customer per period.

Load a marketing use case:

Four cases: a free-trial campaign for a grocery cold brew, a food-delivery app's win-back credits, a pet shop's VIP coupon, and a bookshop whose readers may all be much alike.

Drag & Drop raw data file (.csv, .tsv, .txt)

Long format: one row per customer per period, with a customer id, a period and a yes/no outcome, plus optional driver columns and a segment. CLV's activity panels load as they are. At least 100 customers; at most 100,000 rows.

No file uploaded.

INPUTS & SETTINGS

Step 2Tell the model who, when and what

Pick the column that says who each row is, the column that says when, and the yes/no outcome. Then pick the drivers: things that could change a customer's chance of a "yes" in a given period, such as a coupon. Then say in a word or two what a "yes" is, and whether it is good or bad news: the write-ups use your words.

Customer id

Period (number or date)

Outcome (yes/no) Counts as "yes" Describe a "yes" in a word or two For the business, a "yes" is

Segment (optional)

Drivers

Tick a driver to include it. "Same period" means this period's value; "1 period earlier" means the customer's value in the period before.

Driver	Same period	1 period earlier
Load data to see its columns.

Step 3Decide what the model may know about each customer

Model A treats every customer alike. Model B adds what the data records about each one. Model C also gives every customer their own baseline. Switch pieces off to see what each one does to the habit estimate.

Each customer's first period Each customer's average level of each driver The segment column

Fit model C (random effects)

Held-back periods

Trial horizon (periods)

Advanced

Quadrature nodes (model C)

Decision threshold (accuracy and switches only)

🤔 Try this:

Load Thistledown Market and run with every box ticked. Note the habit effect under A, B and C.
Untick Fit model C and run again. Read the "Start here" box: what can the page no longer tell you?
Load Crave and run. Then untick The segment column and run again. Which model moved, and which did not?

Load a case or upload a panel to begin.

Step 4VISUAL OUTPUT

Start with the customers themselves, then watch the habit estimate change as the model learns more about each one.

Twelve customers, period by period

Each row is one customer and each square one period: dark means a "yes". Rows are sorted from the customers with the most to those with the fewest. These twelve are a random draw from the data.

📊 How to Read This Chart

Long dark rows at the top and nearly empty rows at the bottom are loyalty: customers who differ.
Habit shows up as runs that start after a purchase in customers of every kind, not just the top rows.
Customers who never change say nothing about habit; it rests on those who switch.

Habit or loyalty?

Each bar is how many percentage points a "yes" last period adds to the chance of another this period, under one model, with its 95% interval. If the bar shrinks as the model learns more about each customer, the difference was between customers, not carried over from one period to the next.

📊 How to Read This Chart

Model A treats every customer alike, so it credits all of the loyalty to habit. Its bar is the number a naive analysis would report.
Model C compares each customer with their own usual rate. Its bar is the habit that is left.
If model B lands close to A, the obvious extra columns did not carry the information needed; that is a finding too.

How different are the customers?

The bars count customers by how often they had a "yes" over the fitted periods. The shaded band is model C's middle 80% of customers' chance of a "yes" in a typical period.

📊 How to Read This Chart

A wide spread, often with piles at both ends, is a market where loyalty can explain a lot.
A narrow pile in the middle means customers are much alike; then the three models should agree.

What is a trial worth?

Extra purchases per 100 trials over the trial horizon, among customers who had not bought in the last fitted period. Only real habit makes a trial echo; loyalty does not.

Margin per purchase, in dollars (optional)

📊 How to Read This Chart

Weigh the model C bar against what a trial costs. The model A bar is what a campaign built on the naive analysis would expect.
The count excludes the trial purchase itself: it is what follows.

Does it forecast the same customers' next periods?

Lower is better. Each bar is the average penalty on the held-back periods: a confident miss costs a lot. The bar to beat is each customer's own purchase rate so far.

📊 How to Read This Chart

Model C forecasts each customer from their own history plus the drivers, so it should beat their own rate when the model is right.
"Same as last period" has no bar: it only says 0% or 100%. It appears in the table instead.

Forecast	Log loss	Brier	AUC	Accuracy	Switches caught

Step 5WHAT THIS MEANS

Start with the plain reading, then the two write-ups. The numbers below are the ones to quote.

Habit or loyalty?

–

Habit effect, model C

Run the analysis to see what this means here.

How different are the customers?

–

Middle 80% of usual rates

What is a trial worth?

–

Extra purchases per 100 trials

Does it beat each customer's own history?

–

Holdout log loss vs own rate

Start here

Managerial Interpretation

Run the analysis to see the managerial interpretation.

APA-Style Report

Run the analysis to see the APA-style report.

MODEL DETAILS

Coefficients for the three models (log-odds)

Each cell is a coefficient on the log-odds scale with its standard error in brackets. Don't compare the habit row's odds ratios across columns: model C measures it within each customer and the others across customers. Compare the habit effect in points, in the chart above, instead.

Term	A: every customer alike	B: plus customer terms	C: random effects	C: odds ratio [95% CI]

Customers / customer-periods fitted:–

Log-likelihood, A / B / C:–

Between-customer SD (σ):–

Latent ICC:–

Test that customers differ (σ = 0):–

Quadrature check:–

📊 How to Read This Table

The "last period" row is the habit on the log-odds scale. Watch it fall from A to C in a loyalty-driven market.
The first-period and customer-average rows are not effects. They stand in for each customer's baseline.
A driver whose coefficient falls a lot from A to C went mostly to customers who buy anyway.

DIAGNOSTICS & ASSUMPTIONS

Each check below says what it found and what to do about it. A failed check is a next step, not a verdict on the data.

When it says 30%, does it happen 30% of the time?

Held-back forecasts from the best model, grouped by how confident they were. Points on the diagonal mean the probabilities can be read as real chances; points below mean the model overstated them.

EXPLORATORY QUESTIONS

On Thistledown, the model with each shopper's first week and coupon average barely moves the habit estimate. What information is it missing that model C finds, and where does C find it?
On Crave, the segment column lands model B close to model C. Why would that not have worked on Thistledown?
On Fernhill, the coupon's effect falls between A and C. Write one sentence for the loyalty manager that explains why, without using the word "coefficient".
On Saltmarsh, the three models agree. Is that a disappointing result or a useful one? Why?
A colleague says "just use each customer's own purchase rate as a control". When would that help, and what does it cost?

LEARNING RESOURCES

📚 Going further

Only randomisation settles it: habit versus loyalty is exactly why marketers keep a random holdout group out of trial offers.
Hidden segments: latent-class models drop the bell-curve assumption and find groups of customers no column records.
Counts instead of yes/no: units per week need a count model built on the same idea.

Panel Dynamic Logistic Regression

👨‍🏫 Professor Mode: Guided Learning Experience

QUICK START: Choose Your Path

Try an Example

Analyze My Data

Learn the Idea

OVERVIEW & WHAT THIS TOOL SOLVES

🎯 Questions It Answers

📂 What Data You Need

💡 What You'll Discover

Step 1DATA SOURCE

Use a Case Study

Upload Your Data

INPUTS & SETTINGS

Step 2Tell the model who, when and what

Drivers

Step 3Decide what the model may know about each customer

Step 4VISUAL OUTPUT

Twelve customers, period by period

Habit or loyalty?

How different are the customers?

What is a trial worth?

Does it forecast the same customers' next periods?

Step 5WHAT THIS MEANS

Start here

Managerial Interpretation

APA-Style Report

MODEL DETAILS

Coefficients for the three models (log-odds)

REVEAL THE TRUTH

DIAGNOSTICS & ASSUMPTIONS

When it says 30%, does it happen 30% of the time?

EXPLORATORY QUESTIONS

LEARNING RESOURCES