Monte Carlo Sizing & BIBD Randomization

@glanegonsalves

Hey there Glane here, I can develop the complete reproducible Monte Carlo sample-size simulation in R, using a conditional logit framework to evaluate the 95% CI half-width targets of 0.5, 0.4, and 0.3 for the difference between the highest and second-highest preference weights. I’ll include convergence and stopping rules, power curves, sensitivity checks, and clear justification of the final sample sizes. I’ll also construct the required Balanced Incomplete Block Design (12 outcomes × 12 tasks, 4 outcomes per task) and generate a fielding-ready participant randomisation sequence. Deliverables will include annotated R scripts, exported tables/plots, the BIBD task-by-outcome matrix and randomisation file in CSV/Excel, a concise technical memo, and a README allowing the research team to reproduce the full workflow with a single command.

@ronakkataria1

Hi — worth flagging up front: a true BIBD at v=12, k=4, b=12 doesn't exist. Balance requires lambda(v-1)=r(k-1); with r=4 that gives lambda=12/11, not an integer. What you can have is a near-balanced resolvable design where each outcome appears 4 times and pair frequencies differ by at most one. Standard for BWS and defensible — but it belongs in the memo, not found by a reviewer. On the simulation: - Generate choice sets from the design, simulate responses under assumed utility weights, fit conditional logit (survival::clogit or mlogit), extract the CI half-width for the top-vs-second difference, repeat across sample sizes. - Assumed effect size drives everything. I'd run a grid of plausible weight separations rather than one guess, so the recommendation isn't an artefact of one assumption. - Convergence checked on every fit; non-converged replicates reported, not silently dropped — dropping them biases power upward. - Stopping rule: smallest n where the proportion of replicates meeting the half-width target crosses your threshold, with Monte Carlo error on that proportion shown. Deliverables as specified: annotated R scripts, tables and power curves, technical memo, BIBD matrix plus randomisation CSV, single-command README. Questions: 1. Assumed weight separation, or shall I propose a grid? 2. Target power — 80% or 90%? 3. Which fielding software consumes the randomisation list? Ronak — 8+ yrs data science; R and Python, simulation and experimental design.