• Code, plots, and this presentation are organized and hosted in a github repository.
• The repository includes steps to reproduce the dataset and models.
• The data for this project are privately owned and not available on the repository at this time.

Summary

• Differences in variation between the trials suggest that it may be possible to build a model capable of predicting a texting event.
• Subject specific plots are unique enough that a variable for each subject may be needed in modeling.

Baseline Trial

• Trial 4 was used as a baseline trial because the conditions were identical to the Texting Trial (dense traffic with detour).
• The overall mean for each subject's emotion in the Baseline Trial was subtracted from every observation in the Texting Trial.
  

Model Proposal

• Train a Feed Forward Neural Network using emotional likelihoods and demographics to predict when a subject is texting.

Neural Network Advantages

• Neural Networks (nnet) are well suited for large datasets of continuous variables.
• Nnets are analogous to logistic regression and appropriate for predicting probabilities.

Tenets of Feed-Forward Neural Networks:

• Class of statistical learning model;
• Uses a training set for tuning the model and a testing set for measuring performance;
• Similar to logistic regression;
• Typically displayed as a diagram of connected nodes.

Neural Network Components

• Nodes:
  • Input Nodes: Input values of the predictor variables;
  • Hidden and Output Nodes: Values are the sum product of the connected weights and nodes values.
• Weights:
  • Represents the transformation that takes place between nodes.
• Activation Function:
  • Transforms the output into an appropriate scale.
  • For logistic regression, the sigmoid function: \( S(x) = \frac{1}{1 + \exp(-x)} \)

Step 1: Model is initialized with random weights.

Step 2: Calculate hidden weights and output node prediction.

• Hidden node values are the sum product of the connected weights and input nodes:

• Output node prediction:

• Model Error: .739

• Update weights between the hidden layer and output node:

• Update weights between the input nodes and hidden layer:

Step 4: Repeat Step 2 to update the hidden nodes and output prediction.

• S(.633) = .653, Error = .653 vs previous .739

First Iteration of a Basic Neural Network

General Model Form

\[ \begin{align*} nnet(Texting \sim & \text{ } Subject + Age + Gender + Anger + Contempt \text{ } + \\ & \text{ } Digust + Fear + Joy + Sad + Surprise + Neutral)\\ \end{align*} \]

Modeling Strategy

## Set Cross Validation
fit.control = trainControl(method = "cv", number = 10)

## Create model parameters
search.grid = expand.grid(decay = c(0, .1, .2), 
                          size = c(1, 10, 25, 50))

## Limit the iterations and weights
maxIt = 1000; maxWt = 15000

fit = train(Texting ~ . - Time, mdl.08.train, 
            method = "nnet",
            trControl = fit.control,
            tuneGrid = search.grid,
            MaxNWts = maxWt,
            maxit = maxIt)

40255 samples, 12 predictors, 2 classes: '0', '1' 

Resampling: Cross-Validated (10 fold) 
Summary of sample sizes: 436229, 36229, 36229, ...
Resampling results across tuning parameters:

  ------------------------------
  Decay  Size  Accuracy   Kappa
  ------------------------------
  0.0     1    0.643      0.302
  0.0    10    0.793      0.566
  0.0    25    0.819      0.625
  0.0    50    0.833      0.655
  0.1     1    0.667      0.306
  0.1    10    0.814      0.612
  0.1    25    0.834      0.655
  0.1    50    0.841      0.669
  0.2     1    0.681      0.310
  0.2    10    0.814      0.611
  0.2    25    0.830      0.646
  0.2    50    0.834      0.654

• 13 of 56 had testing performance > 90%
• 36 of 56 had testing performance > 80%
• 5 of 56 had testing performance < 70%
• 5 of the 6 worst performaning Subjects were Old (1 Male, 4 Female)

******************************************************************
Levene's Test for Homogeneity of Variance (Center = Median)
******************************************************************
      Df F value Pr(>F)
group  1  0.7054 0.4047
      54  

******************************************************************
General Linear Model
******************************************************************
Deviance Residuals: 
     Min        1Q    Median        3Q       Max  
-0.18434  -0.06279   0.01139   0.05423   0.16550 

Coefficients:   Estimate Std. Error t value Pr(>|t|)    
(Intercept)     0.77983    0.02471  31.558   <2e-16 ***
Old Male        0.04272    0.03302   1.294   0.2015    
Young Female    0.07307    0.03171   2.304   0.0252 *  
Young Male      0.05548    0.03302   1.680   0.0989 . 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for gaussian family taken to be 0.006717054)

    Null deviance: 0.38640  on 55  degrees of freedom
Residual deviance: 0.34929  on 52  degrees of freedom
AIC: -115.4

******************************************************************
Shapiro-Wilk Normality Test
******************************************************************
data:  mdl$residuals
W = 0.98393, p-value = 0.6586