The Originative Statistical Regression Models: Are They Too Old and Untenable? To Fit or Not to Fit Data to a Model: That is the Question.

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2 Objectives 1.To poll the titled and untitled questions. 2.To offer my answer with illustrative examples (2) and recent projects (2). The Originative Statistical Regression Models: Are They Too Old and Untenable? To Fit or Not to Fit Data to a Model: That is the Question.

3 Are They Too Old and Untenable? For big data apps, yes. And small data apps, as well. Statistical ordinary least squares (OLS) regression, and logistic regression (LR) models are popular techniques for prediction (of a continuous dependent variable) or classification (of a categorical dependent variable). They are the workhorses of statistical modeling as their results are considered the gold standard. Moreover, they are used as the benchmark for assessing the superiority of newer techniques. OLS regression method was first published by Legendre on March 6, The LR model was developed by Berkson in Something old is not necessarily useless today, and something new is not necessarily better than something old is. Lest one forgets, "the wheel and the printed word." The statistical regression paradigm, which dictates "fitting the data to a pre-specified model," is old as it was developed, and tested within the small data setting of the day. It would seem that a newer machine-learning method, say, GenIQ, which "lets the data define the model," is especially effective for today's big data, and should nicely outdo the originative statistical regression model.

4 To Fit Data to a Model? For experimental-design and clinical data, yes. For post-hoc, secondary and big data, I do not think so. The linear model for one and for all, no.

5 In this illustration, GenIQs optimizing of the deciles is equivalent to predicting the best possible ranking of the target variable based on the GenIQ score GenIQvar. Bruce Ratner, Ph.D. 5

6 OBJECTIVE #1: To build a binary response model with data from Table 1. I built a logistic regression model (LRM) for predicting the target variable Response using two predictor variables, XX1 and XX2. The LRM equation is: Logit of Response (=Yes) = * XX * XX2 Table 1 ID XX1 XX2 Response Yes No Yes No No No Yes Yes Yes No Bruce Ratner, Ph.D. 6

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11 OBJECTIVE: To build a continuous profit model with data from Table 1. I built an ordinary least squares regression model (OLS) for predicting the target variable Profit using two predictor variables, XX1 and XX2. The OLS equation is: Profit_est = * XX * XX2 Table 1 ID XX1 XX2 Profit Bruce Ratner, Ph.D. 11

12 OLS RESULTS: The Profit ranking is not perfect. The ranking of Profit based on the OLS Profit score, Profit_est, is in Table 2, below. Clearly, the Profit ordering is not perfect. Table 2 ID XX1 XX2 Profit Profit_est Bruce Ratner, Ph.D. 12

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15 I built a GenIQ Model to predict Profit using XX1 and XX2 with data in Table 1. The GenIQ Model tree display and model equation (code) are below. Note: There are two GenIQ variables, GenIQvar_1, GenIQvar_2 (defined later). x1 = GenIQvar_1; x1 = Cos(x1); x2 = GenIQvar_2; x1 = x1 * x2; x2 = XX2; x2 = Cos(x2); x2 = Cos(x2); x3 = GenIQvar_2; x4 = GenIQvar_2; x3 = x3 * x4; x2 = x3 - x2; x1 = x1 * x2; GenIQvar = x1; Bruce Ratner, Ph.D. 15

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17 RECENT PROJECT #1 Objective Dec 06 Sep 08 Aug 10 Dec 11 To build a LTV5 Model based on sales transaction data from Dec., 2006 Dec., 2011 The window of Sep 08 Aug 10 is for defining the ATTRITION and LVT5 variables ATTRITION = 1 if there are no sales in the monthly window = 0 if there is at least one sale in the mos wndw LTV5 = LVT2*2.5 where LTV2 = total sales in the mos wndw In addition to monthly sales, which reflect few big-ticket items and many $0s, the three basic variables are also put in play for machine-learning data mining (Predictors are defined in Dec 06 Aug 08): 1. RECENCY = last month in which a sale occurrence was observed for a rep. 2. TRX = total number of monthly sales transactions observed 3. BEGYR = first year in which a sales occurrence was observed

18 Identification of the Relationships that Define Attrition(=1-Retention) and LTV5 Machine-learning data mining identifies surprising relationships ATTRITION_var = RECENCY TRX*BEGYR LTV5_var = TRX*BEGYR RECENCY

19 x1 = TRX; x2 = begyr; x1= x1 * x2; x2 = Recency; If x1 NE 0 Then x1 = x2 / x1; Else x1 = 1; GenIQvar = x1; GenIQ_ATTRITION_probability = 1 / (1 + Exp(-( GenIQvar * )));

20 x1 = TRX; x2 = TRX; x3 = begyr; x2 = x2 * x3; If x1 NE 0 Then x1 = x2 / x1; Else x1 = 1; x2 = Recency; x3 = TRX; If x2 NE 0 Then x2 = x3 / x2; Else x2 = 1; x1 = x1 * x2; GenIQvar = x1; GenIQ_Profit_estimate = * GenIQvar;

21 Identification of the Relationships that Define Attrition(=1-Retention) and LTV5 Estimating the vars, we have Logit_ATTRITION = (2.1622*ATTRITION_var) PROB_ATTRIT_est = exp(logit_attrition)/(1+ exp(logit_attrition) ) LTV5_var = (TRX*BEGYR)/RECENCY LTV5_estimate = ( *LTV5_var)

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26 RECENT PROJECT #2 Objective To build a classification model based on survey data, where the dependent variable focuses on three segments of the original six segments (1, 2,, 6) _3, _4 and _1256

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29 Defining the Classification Model Prob_3_1256 = 1 / (1 + Exp(-( GenIQvar * ))); logit_3_1256 = GenIQvar * ; PROB_4_1256 = 1 / (1 + Exp(-( GenIQvar * E-02))); logit_4_1256= GenIQvar * E-02; Prob_3 = exp(logit_3_1256)/ (1 + exp(logit_3_1256) + exp(logit_4_1256) ); Prob_4 = exp(logit_4_1256)/ (1 + exp(logit_3_1256) + exp(logit_4_1256) ); Prob_1256 = 1 - ( Prob_3 + Prob_4);

30 Classification Model Accuracy

31 Marginal Model (set Prob_1256=0)

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