Training Dataset

Check Data types and Missing values

The datasets both have missing values. There are 3 categorical variables (LabelAppeal,AcidIndex,STARS), 11 continuous variables and the target variable is categorical.

Missing Values and Data Type Check

Missing Values and Data Type Check

Data Statistics Summary

A binary logistic regression model is built using the training set, therefore the training set is used for the following data exploration.

The data types in the raw dataset are all ‘doubles’, however the counter INDEX and the response variable target are categorical.

The statistics of all variables are listed below:

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    StdD    Skew    Kurt 
##    0.00    2.00    3.00    3.03    4.00    8.00    1.93   -0.33   -0.88

Response Variable

Upon examining the target variable we immediately see a normal distribution save for the large number of unsold cases.

Model 1: Poisson Model without imputations

(Dispersion parameter for poisson family taken to be 1 )

Stars and Label appeal seem to have a strong positive impact on sales, which is to be expected (and will be seen in all models). On the acid front the acidindex value seems a better predictor than the acid components. ### Model 2: Poisson Model without imputations and only significant variables

(Dispersion parameter for poisson family taken to be 1 )

Reducing the variables in the model doesn’t have a major impact on the model, and will probably improve its performance in actual fact.

Model 3: Poisson Model with imputations

(Dispersion parameter for poisson family taken to be 1 )

With imputations a number of variables become significant, including acidity, and Sulfur/sulphate counts. This makes some intuitive sense as those would affect the taste of the wine. Interestingly, the coefficient is positive on the sulfur dioxide. One would rarely expect sulfur dioxide (the smell of burnt matches) to be an improvement for wine.

Model 4: Poisson Model with imputations and only significant variables

(Dispersion parameter for poisson family taken to be 1 )

Using just the significant variables we do not get much of an improvement in AIC, but the model seems to lose little. ## Model II: Negative Binomial Model

Model 5 : Negative Binomial Model without imputations

## 
## Call:
## glm.nb(formula = TARGET ~ ., data = wine_train1, init.theta = 138898.9107, 
##     link = log)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -3.2127  -0.2757   0.0647   0.3766   1.6981  
## 
## Coefficients:
##                      Estimate Std. Error z value Pr(>|z|)    
## (Intercept)         1.608e+00  2.796e-01   5.750 8.91e-09 ***
## FixedAcidity        6.705e-04  1.177e-03   0.570  0.56900    
## VolatileAcidity    -2.750e-02  9.283e-03  -2.963  0.00305 ** 
## CitricAcid         -3.835e-03  8.519e-03  -0.450  0.65259    
## ResidualSugar       1.828e-05  2.152e-04   0.085  0.93231    
## Chlorides          -3.764e-02  2.314e-02  -1.627  0.10378    
## FreeSulfurDioxide   5.671e-05  4.892e-05   1.159  0.24630    
## TotalSulfurDioxide  2.230e-05  3.177e-05   0.702  0.48275    
## Density            -4.025e-01  2.750e-01  -1.464  0.14326    
## pH                  2.307e-04  1.085e-02   0.021  0.98303    
## Sulphates          -5.984e-03  7.973e-03  -0.751  0.45293    
## Alcohol             3.262e-03  2.004e-03   1.628  0.10360    
## LabelAppeal         1.730e-01  8.858e-03  19.529  < 2e-16 ***
## AcidIndex          -4.967e-02  6.666e-03  -7.451 9.28e-14 ***
## STARS               1.929e-01  8.328e-03  23.160  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for Negative Binomial(138898.9) family taken to be 1)
## 
##     Null deviance: 4720.4  on 5143  degrees of freedom
## Residual deviance: 3242.7  on 5129  degrees of freedom
##   (5093 observations deleted due to missingness)
## AIC: 18547
## 
## Number of Fisher Scoring iterations: 1
## 
## 
##               Theta:  138899 
##           Std. Err.:  259921 
## Warning while fitting theta: iteration limit reached 
## 
##  2 x log-likelihood:  -18515.07

AIC is similar to Poisson without imputations, as are some of the coefficients. ### Model 6 : Negative Binomial Model without imputations and only significant variables

## 
## Call:
## glm.nb(formula = TARGET ~ . - FixedAcidity - CitricAcid - ResidualSugar - 
##     Chlorides - FreeSulfurDioxide - TotalSulfurDioxide - Density - 
##     pH - Sulphates - Alcohol, data = wine_train1, init.theta = 138402.5261, 
##     link = log)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -3.1898  -0.2777   0.0622   0.3764   1.6086  
## 
## Coefficients:
##                  Estimate Std. Error z value Pr(>|z|)    
## (Intercept)      1.251443   0.054725  22.868  < 2e-16 ***
## VolatileAcidity -0.027581   0.009279  -2.973  0.00295 ** 
## LabelAppeal      0.173177   0.008853  19.562  < 2e-16 ***
## AcidIndex       -0.050616   0.006553  -7.724 1.13e-14 ***
## STARS            0.194209   0.008292  23.421  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for Negative Binomial(138402.5) family taken to be 1)
## 
##     Null deviance: 4720.4  on 5143  degrees of freedom
## Residual deviance: 3253.0  on 5139  degrees of freedom
##   (5093 observations deleted due to missingness)
## AIC: 18537
## 
## Number of Fisher Scoring iterations: 1
## 
## 
##               Theta:  138403 
##           Std. Err.:  258834 
## Warning while fitting theta: iteration limit reached 
## 
##  2 x log-likelihood:  -18525.37

Removing non significant variables doesn’t seem to affect the model’s accuracy much. ### Model 7 : Negative Binomial Model with imputations

## 
## Call:
## glm.nb(formula = TARGET ~ ., data = wine_train2, init.theta = 49067.84702, 
##     link = log)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -2.9896  -0.6852   0.1295   0.6351   2.4377  
## 
## Coefficients:
##                      Estimate Std. Error z value Pr(>|z|)    
## (Intercept)         2.350e+00  2.280e-01  10.307  < 2e-16 ***
## FixedAcidity        2.238e-04  9.202e-04   0.243 0.807848    
## VolatileAcidity    -4.578e-02  7.287e-03  -6.282 3.34e-10 ***
## CitricAcid          6.770e-03  6.566e-03   1.031 0.302510    
## ResidualSugar       1.586e-04  1.674e-04   0.947 0.343463    
## Chlorides          -6.268e-02  1.794e-02  -3.494 0.000476 ***
## FreeSulfurDioxide   1.249e-04  3.801e-05   3.285 0.001020 ** 
## TotalSulfurDioxide  8.362e-05  2.457e-05   3.403 0.000666 ***
## Density            -3.887e-01  2.145e-01  -1.813 0.069902 .  
## pH                 -1.990e-02  8.406e-03  -2.367 0.017923 *  
## Sulphates          -1.035e-02  6.173e-03  -1.677 0.093603 .  
## Alcohol             2.527e-03  1.557e-03   1.623 0.104549    
## LabelAppeal         1.429e-01  6.779e-03  21.084  < 2e-16 ***
## AcidIndex          -7.543e-01  4.005e-02 -18.832  < 2e-16 ***
## STARS               3.433e-01  6.241e-03  54.998  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for Negative Binomial(49067.85) family taken to be 1)
## 
##     Null deviance: 18290  on 10236  degrees of freedom
## Residual deviance: 12766  on 10222  degrees of freedom
## AIC: 38357
## 
## Number of Fisher Scoring iterations: 1
## 
## 
##               Theta:  49068 
##           Std. Err.:  63120 
## Warning while fitting theta: iteration limit reached 
## 
##  2 x log-likelihood:  -38324.77

With imputations we find surprisingly similar results to a the Poisson model with imputations. ### Model 8 : Negative Binomial Model with imputations and only significant variables

Quitting from lines 354-357 (Wine_Sales.Rmd) Error in data.frame(Observations = length(x\(residuals), `Residual Std. Error` = x\)sigma, : arguments imply differing number of rows: 1, 0 Calls: … pandoc.table -> cat -> pandoc.table.return -> data.frame In addition: There were 45 warnings (use warnings() to see them)

Model 9 : Linear Model with imputations

Use imputed training data on Linear regression model

A plain linear regression model is a surprisingly decent performer when coupled with imputations. ### Model 10 : Linear Model with imputations and only significant variables.

We got FixedAcidity, CitricAcid and ResidualSugar as significant variables and use same variables on Linear regression model with imputed training data.

Again, removing less significant variables has little impact on the model, and is recommended to reduce overfitting. ## Model 11 : Ordinal Logistic Regression

Since Ordinal logistic regression uses ordered factors we might find this as one of the top model based on our use cases.

Call: polr(formula = TARGET ~ ., data = polrDF, Hess = TRUE)

Residual Deviance: 29978.30

AIC: 30022.30

Predicted Evaluation data

https://github.com/ShovanBiswas/DATA621/blob/master/Homework05/Evaluation_Full_Data.csv