Logistic Regression Case - Handlooms

Sales of Handloom Saris An Application of Logistic Regression Objectives • Illustrate importance of interpretation, domain insights from managers for interpretation and implementation • Relevance to situations where too many products (or services) but can define more stable underlying characteristics of products (or services) • Logistic Regression as a tool that parallels multiple linear regression in practice. Powerful analysis in a spreadsheet 1 Handloom Industry in India • Decentralized, traditional, rural, co-ops • Direct employment of 10 million persons • Accounts for 30% of total textile production Co-optex (Tamilnadu State) • Large: 700 outlets; $30million; 400,000 looms • Strengths: – Design variety, short run lengths – Majority sales through co-op shops • Weaknesses: – Competing with mills difficult – Large inventories, high discount sales 2 Study Question • Improve feedback of market to designs through improved product codes • Assess economic impact of proposed code • Pilot restricted to saris – Most difficult – Most valuable A Consumer-oriented Code for Saris • Developed with National Institute of Design 3 Sari components B ody B order Pallav Sari Code B ody:W arp Color & S hade (W R PC, W R PS) W eft C olor & S hade (W FT C, W FT S) B ody Design (B ODD) B order: C olor, S hade, D esign, Size (B R DC, B R DS, B R DD, B R DZ) Pallav: C olor, S hade, D esign, Size (PL V C, PL V S, P L V D, P L V Z) Code Levels • Color (Warp, weft, border, pallav) 10 levels:0=red, 1=blue, 2=green, etc. • Shade (Warp, weft, border, pallav) – 4 levels: 0=light, 1=medium, 2=dark, 3=shiny; • Design (Body, border, pallav) – 23 levels: 0=plain, 1=star buttas, 2=chakra buttas, etc. • Size (Border, pallav) – 3 levels: 0= broad, 1=medium, 2=narrow Assessing Impact Major Marketing Experiment • 14 day high season period selected • 18 largest retail shops selected • 20,000 saris coded, sales during period recorded • Logistic Regression models developed for Pr(sale of sari during period) as function of coded values. 5 Example data (Plain saris) Sari# WrpCI BrdClr WftClr PlvClr WrpS BrdSh WftSh PlvSh BrdDs PlvDs BrdSz PlvSz Response 1 2 2 2 2 2 3 2 3 0 1 0 2 1 2 0 2 0 2 2 3 2 3 0 1 0 0 1 3 0 2 0 2 2 3 2 3 0 1 1 2 1 4 1 2 1 2 0 3 0 3 0 1 1 2 1 5 1 2 1 8 1 3 1 3 0 1 0 1 1 6 4 2 4 8 2 3 2 3 0 1 0 1 1 7 0 1 3 2 0 2 2 3 0 1 0 1 0 8 1 2 1 2 2 3 2 3 0 1 0 1 1 9 1 2 1 2 0 3 0 3 1 1 2 2 1 10 4 2 2 2 1 3 1 3 1 1 2 2 1 11 1 1 1 2 0 2 0 3 0 1 0 2 1 Logistic Regression Model • Odds(Sale) =exp(ß0+ ß1WRPC_1 + ß2WRPC_2 + ß3WRPC_3 + ß4WRPC_4 + ß5PLVD_1 + ß6BRDZ_1+ ß7BRDZ_2) 6 Coefficient Estimates Coeff -0.698 0.195 -2.220 -2.424 -0.072 1.866 -0.778 -0.384 Variable Constant WrpCI_1 WrpCI_2 WrpCI_3 WrpCI_4 PlvDs_1 BrdSz_1 BrdSz_2 Odds 1.215 0.109 0.089 0.931 6.462 0.459 0.681 Confusion Table (Cut-off probability = 0.5) Actual Sale Sale Predicted No Sale Total No Sale Total 15 5 20 5 32 37 20 37 57 7 Impact • Producing only saris that have predicted probability > 0.5 will reduce slow-moving stock substantially. In the example, slowmoving stock will go down from 65% of production to 25% of production • Even cut-off probability of 0.2 reduces slow stock to 49% of production Insights • Certain colors and combinations sold much worse than average but were routinely produced (e.g. green, border widths-body color interaction) • Converse of above (e.g. plain designs, light shade body) • Above adjustments possible within weavers’ skill and equipment constraints • Huge potential for cost savings in silk saris • Need for streamlining code, training to code. 8 Reasons for versatility of Logistic Regression Models in Applications • Derivable from random utility theory of discrete choice • Intuitive model for choice-based samples and case-control studies • Derivable from latent continuous variable model • Logistic Distribution indistinguishable from Normal within ±2 standard deviations range • Derivable from Normal population models of discrimination (pooled covariance matrix) • Fast algorithms • Extends to multiple choices (polytomous regression) • Small sample exact analysis useful for rare events (e.g. fraud, accidents, lack of relevant data, small segment of data) 9