Employee Involvement

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.title[
# Employee Involvement
]
.author[
### Gianna LaFrance, Jaiden Neff, & Samantha Gouveia
]

---

<h1 align = "center"> Table of Contents </h1>
<center><font size="7">  
- Introduction <br>
- Exploratory Data Analysis <br>
- Principal Componenet Analysis <br>
- Multinomial Logistic Regression <br>
- Conclusion & Discussion
</font></center>

---

## Introduction

Our goal for this study is to see the effect that factors have on the overall job involvement at our company. We plan to run statistical tests and observe the data to draw conclusions that will lead us to make informed decisions about how to improve job involvement.

The data set has 1470 rows and 35 columns.

We will be focusing on the following variables for our exploratory data analysis and we will keep these for our sample population.

- Job Involvement: Likert scale 1-4 from low to very high
- Environment Satisfaction: Likert scale 1-4 from low to very high
- Job Satisfaction: Likert scale 1-4 from low to very high
- Work Life Balance:Likert scale 1-4 from low to very high
- Monthly Income:
- Years Since Last Promotion:
- Years At Company:
- Age:
- Number Companies Worked:
- Department:
- Job Level:
- Years With Current Manager:
- Hourly Rate:

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# Exploratory Data Analysis

---

## Job Involvement Data

```
## Frequency Distribution of Job Involvement:
```

```
## 
##   1   2   3   4 
##  83 375 868 144
```

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## Frequency Graphics

---

## Frequency Graphics

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## Summary Statistics

```
## 
## Summary statistics for Hourly Rate:
```

```
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   30.00   48.00   66.00   65.89   83.75  100.00
```

```
## 
## Summary statistics for Years Since Last Promotion:
```

```
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   0.000   0.000   1.000   2.188   3.000  15.000
```

```
## 
## Summary statistics for Age:
```

```
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   18.00   30.00   36.00   36.92   43.00   60.00
```

```
## 
## Summary statistics for Number of Companies Worked For:
```

```
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   0.000   1.000   2.000   2.693   4.000   9.000
```

---

## Scatter Plot for Age

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## Job Involvemnet and Satisfaction

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## Department

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## Correlation Plot

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## Correlation Coefficents

```
##          JobInvolvement EnvironmentSatisfaction         JobSatisfaction 
##             1.000000000            -0.008277598            -0.021475910 
##           MonthlyIncome YearsSinceLastPromotion          YearsAtCompany 
##            -0.015271491            -0.024184292            -0.021355427 
##         WorkLifeBalance                     Age      NumCompaniesWorked 
##            -0.014616593             0.029819959             0.015012413 
##                JobLevel    YearsWithCurrManager              HourlyRate 
##            -0.012629883             0.025975808             0.042860641
```

---

## Findings

We found that there are not that many factors that are highly correlated with Job Involvement there are a few however that have higher correlations and that we will be including in the Final Model

Multicollinearity in monthly income and job level and Years at Company and Years with Current Manager so we removed these factors because they were not significant on their own

Monthly Income and Hourly Rate are not correlated which I thought was interesting

A lot of the variables are more highly correlated to each other than they are to the variable Job Involvement

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# Principal Component Analysis

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## PCA

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## Factor Loading

Table: Factor loadings of the first few PCAs and the cumulative proportion
of variation explained by the corresponding PCAs in the employee survey.

|                        |    PC1|    PC2|
|:-----------------------|------:|------:|
|YearsAtCompany          | -0.539|  0.327|
|YearsSinceLastPromotion | -0.475|  0.328|
|JobInvolvement          |  0.013| -0.143|
|JobSatisfaction         |  0.017|  0.137|
|WorkLifeBalance         | -0.013|  0.062|
|Age                     | -0.440| -0.426|
|NumCompaniesWorked      | -0.102| -0.737|
|MonthlyIncome           | -0.528| -0.133|

---

## Proportion of Variation Explained

Table: Cumulative and proportion of variances explained by each 
    the principal component in the employee survey.

|                       |   PC1|   PC2|
|:----------------------|-----:|-----:|
|Standard deviation     | 1.510| 1.133|
|Proportion of Variance | 0.285| 0.160|
|Cumulative Proportion  | 0.285| 0.445|

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# Multinomial Logistic Regression

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name: colors

## MLR

We used the 4th level as the baseline for Job Involvement.

First, we did a model with all of our variables: 
- Environment Satisfaction: Likert scale 1-4 from low to very high
- Job Satisfaction: Likert scale 1-4 from low to very high
- Work Life Balance:Likert scale 1-4 from low to very high
- Years Since Last Promotion:
- Age:
- Number Companies Worked:
- Department:
- Hourly Rate:

The only variables that were statistically significant were Job Satisfaction, Environment Satisfaction, and Hourly Rate.

---
name: colors

## Model

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```{.scroll-100}
## 
## Call:
## vglm(formula = JobInvolvement ~ ., family = multinomial, data = employee1)
## 
## Coefficients: 
##                            Estimate Std. Error z value Pr(>|z|)    
## (Intercept):1             -0.618707   0.704149  -0.879 0.379586    
## (Intercept):2              1.063167   0.497672   2.136 0.032656 *  
## (Intercept):3              1.569505   0.457687   3.429 0.000605 ***
## JobSatisfaction:1          0.217457   0.128412   1.693 0.090373 .  
## JobSatisfaction:2          0.017965   0.088588   0.203 0.839295    
## JobSatisfaction:3          0.075419   0.081347   0.927 0.353856    
## EnvironmentSatisfaction:1 -0.007483   0.124508  -0.060 0.952078    
## EnvironmentSatisfaction:2  0.148697   0.089249   1.666 0.095693 .  
## EnvironmentSatisfaction:3  0.142680   0.081670   1.747 0.080630 .  
## HourlyRate:1              -0.007772   0.006846  -1.135 0.256260    
## HourlyRate:2              -0.008251   0.004883  -1.690 0.091059 .  
## HourlyRate:3              -0.005292   0.004486  -1.180 0.238188    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Names of linear predictors: log(mu[,1]/mu[,4]), log(mu[,2]/mu[,4]), 
## log(mu[,3]/mu[,4])
## 
## Residual deviance: 3072.792 on 4398 degrees of freedom
## 
## Log-likelihood: -1536.396 on 4398 degrees of freedom
## 
## Number of Fisher scoring iterations: 5 
## 
## No Hauck-Donner effect found in any of the estimates
## 
## 
## Reference group is level  4  of the response
```

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## Model Assumptions

One assumption that needs to be tested is collinearity betweeen the explanatory varibles.

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## Conclusion

Not as many variables were correlated/significant in predicting Job Involvement.

Some of our variables were even negatively correlated.

Job Satisfaction, Environment Satisfaction, and Hourly Rate were significant at the 0.1 alpha level.

Continued work: restructuring PCs to include in the model to get better estimates.

---

## Contributions

Introduction and Exploratory Analysis ~ Jaiden

PCA ~ Samantha

Multinomial Logistic Regression ~ Gianna