Grouped owner

Creating variable in background

Grouped water source

Creating variable in background

Challenge factors

HR challenges, financial-tech challenges

Creating index variables for independent variables based on factor analysis.

HR challenge index: Managerial competence, technical capabilities, manpower and hiring

FT challenge index: Financing operations and maintenance, financing infrastructure, maintaining high water quality, complying with regulations

Distribution of index variables

HR challenge skewed

FT challenge skewed, but not as bad

Benefit average index

I just did this as a starting point for the dependent variable, below I try out a “straight scale” (adding up complete cases). This takes into account incomplete so if someone answered 2 out of 9 their average is taken out of 2.

Very skewed distribution, lots of zeros.

Regression

Prep data

Median income looks a little more normal to me than percent poverty, and so I try out percent poverty but use median income in most models below. I need to think through implications of one variable over another.

Model 1 average benefit index, poverty level

Using two challenge index variables

#Regression table with poverty prevalence

Model 2 median income

Model 3 EPA region added and median income

##Looking at EPA region

##  Region 1 Region 10  Region 2  Region 3  Region 4  Region 5  Region 6  Region 7 
##       470       480       229       541       688       929       633       633 
##  Region 8  Region 9 
##       464       552

#Regression Table models 1, 2 and 3

Table 2. Regression Results Model 2 and 3
Dependent variable:
Benefit Index
Model 2 Median Income Model 3 Median Income and EPA Region
(1) (2) (3)
HR_Chal_Index 0.31*** 0.31*** 0.31***
(0.02) (0.02) (0.02)
Fin_Tech_Chal_Index 0.24*** 0.24*** 0.24***
(0.02) (0.02) (0.02)
Challenge_Customer 0.07*** 0.07*** 0.07***
(0.02) (0.02) (0.02)
grouped_owner1Privately Owned -0.01 -0.02 -0.05
(0.04) (0.04) (0.04)
grouped_owner1Community Owned -0.01 -0.03 -0.05
(0.04) (0.04) (0.04)
grouped_owner1Other -0.05 -0.06 -0.09
(0.09) (0.09) (0.09)
grouped_water_sourcePurchased 0.18*** 0.18*** 0.20***
(0.04) (0.04) (0.04)
grouped_water_sourceSurface water 0.02 0.04 0.03
(0.05) (0.05) (0.06)
percent_below_poverty_level 0.0004
(0.002)
median_income 0.0000*** 0.0000**
(0.0000) (0.0000)
Population_Served_Count -0.0000*** -0.0000*** -0.0000***
(0.0000) (0.0000) (0.0000)
NEAR_DIST -0.0000* -0.0000* -0.0000+
(0.0000) (0.0000) (0.0000)
EPA_RegionRegion 10 -0.15*
(0.07)
EPA_RegionRegion 2 -0.04
(0.08)
EPA_RegionRegion 3 -0.19**
(0.06)
EPA_RegionRegion 4 -0.11+
(0.06)
EPA_RegionRegion 5 -0.21***
(0.06)
EPA_RegionRegion 6 -0.20**
(0.06)
EPA_RegionRegion 7 -0.24***
(0.06)
EPA_RegionRegion 8 -0.20**
(0.07)
EPA_RegionRegion 9 -0.15*
(0.06)
Constant 0.38*** 0.26*** 0.45***
(0.04) (0.05) (0.08)
Observations 4,179 4,171 4,171
Adjusted R2 0.29 0.29 0.29
Note: (+ p<0.1; * p<0.05; ** p<0.01; *** p<0.001)

Diagnostics model 1, 2 and 3

Diagnostics model 1

Pattern in the residuals which is expected with a limited dependent variable. May need to think about other models, but using these results to just get started

## 
##  Asymptotic one-sample Kolmogorov-Smirnov test
## 
## data:  rz_full_1
## D = 0.07, p-value <0.0000000000000002
## alternative hypothesis: two-sided

Diagnostic Model 2

##                         GVIF Df GVIF^(1/(2*Df))
## HR_Chal_Index            1.6  1             1.3
## Fin_Tech_Chal_Index      1.7  1             1.3
## Challenge_Customer       1.4  1             1.2
## grouped_owner1           1.4  3             1.1
## grouped_water_source     1.2  2             1.0
## median_income            1.1  1             1.0
## Population_Served_Count  1.3  1             1.1
## NEAR_DIST                1.1  1             1.1

## 
##  Asymptotic one-sample Kolmogorov-Smirnov test
## 
## data:  rz_full_2
## D = 0.07, p-value <0.0000000000000002
## alternative hypothesis: two-sided

Diagnostic Model 3

##                         GVIF Df GVIF^(1/(2*Df))
## HR_Chal_Index            1.6  1             1.3
## Fin_Tech_Chal_Index      1.7  1             1.3
## Challenge_Customer       1.4  1             1.2
## grouped_owner1           1.5  3             1.1
## grouped_water_source     1.2  2             1.1
## median_income            1.2  1             1.1
## Population_Served_Count  1.3  1             1.1
## NEAR_DIST                1.2  1             1.1
## EPA_Region               1.5  9             1.0

## 
##  Asymptotic one-sample Kolmogorov-Smirnov test
## 
## data:  rz_full_3
## D = 0.07, p-value <0.0000000000000002
## alternative hypothesis: two-sided

CART

Regression tree managerial competence capacity benefit

I think classification trees make more sense with the likert-scale data, but many of the classification trees did not split. Which means there was no way to split the data to improve “predication” of each class. I assume because there are so many zeros (see histograms) there’s no way to split the data that improves prediction more than just guessing 0. Even the classification trees that do split, there’s a decent amount of ‘impurity’ in the leaves.

Because many of the classification trees didn’t split, I also just ran regression trees for everything too. Just to see. Not surprisingly, very difficult to understand systems that see high benefits, often the highest average for a leaf is 2.5.

To classify cases by the level of different operational benefits, most trees use the “corresponding” challenge to split the data set. With higher levels of the corresponding challenge leading to leaves with higher perception of benefits. Some trees have interactions with challenges, and a couple have other “control” variables in the split.

Classification tree managerial competence capabilities benefit

Regression tree technical capabilities benefit

Classification tree technical capabilities benefit

Regression tree manpower benefit

Classification tree manpower benefit

Regression tree hiring benefit

Classification tree hiring benefit

Regression tree admin costs benefit

Classification tree admin costs benefit

Regression tree access to financial resources benefit

Classification tree access to financial resources benefit

## Regression tree water supply benefit

Classification tree water supply benefit

Regression tree unexpected events benefit

Classification tree unexpected events benefit

Benefit row sum index

Just tried an additive scale here (complete cases only), to see if more variation

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
##     0.0     3.0     9.0    10.6    17.0    36.0    1437

Model 4 additive benefit index

## 
## Call:
## lm(formula = partnership_ben_add_index ~ HR_Chal_Index + Fin_Tech_Chal_Index + 
##     Challenge_Customer + grouped_owner1 + grouped_water_source + 
##     median_income + Population_Served_Count + NEAR_DIST + EPA_Region, 
##     data = dat)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -26.47  -4.80  -1.12   4.24  32.78 
## 
## Coefficients:
##                                      Estimate  Std. Error t value
## (Intercept)                        3.57989821  0.68178526    5.25
## HR_Chal_Index                      2.73849623  0.14546786   18.83
## Fin_Tech_Chal_Index                2.23867815  0.15923739   14.06
## Challenge_Customer                 0.66240863  0.15174598    4.37
## grouped_owner1Privately Owned     -0.26455520  0.36635499   -0.72
## grouped_owner1Community Owned     -0.44847008  0.34376745   -1.30
## grouped_owner1Other               -0.77880405  0.81655229   -0.95
## grouped_water_sourcePurchased      1.65137006  0.34485988    4.79
## grouped_water_sourceSurface water  0.33259036  0.49945253    0.67
## median_income                      0.00001447  0.00000533    2.71
## Population_Served_Count           -0.00039553  0.00007029   -5.63
## NEAR_DIST                         -0.00004158  0.00002296   -1.81
## EPA_RegionRegion 10               -1.00104757  0.59649622   -1.68
## EPA_RegionRegion 2                -0.28201234  0.76314870   -0.37
## EPA_RegionRegion 3                -1.36018989  0.58625521   -2.32
## EPA_RegionRegion 4                -0.88854617  0.58130321   -1.53
## EPA_RegionRegion 5                -1.56802875  0.52846250   -2.97
## EPA_RegionRegion 6                -1.41372603  0.57746831   -2.45
## EPA_RegionRegion 7                -1.78928678  0.56812747   -3.15
## EPA_RegionRegion 8                -1.50306767  0.61240780   -2.45
## EPA_RegionRegion 9                -0.95907379  0.57329217   -1.67
##                                               Pr(>|t|)    
## (Intercept)                                 0.00000016 ***
## HR_Chal_Index                     < 0.0000000000000002 ***
## Fin_Tech_Chal_Index               < 0.0000000000000002 ***
## Challenge_Customer                          0.00001303 ***
## grouped_owner1Privately Owned                   0.4703    
## grouped_owner1Community Owned                   0.1921    
## grouped_owner1Other                             0.3403    
## grouped_water_sourcePurchased               0.00000174 ***
## grouped_water_sourceSurface water               0.5055    
## median_income                                   0.0067 ** 
## Population_Served_Count                     0.00000002 ***
## NEAR_DIST                                       0.0702 .  
## EPA_RegionRegion 10                             0.0934 .  
## EPA_RegionRegion 2                              0.7117    
## EPA_RegionRegion 3                              0.0204 *  
## EPA_RegionRegion 4                              0.1265    
## EPA_RegionRegion 5                              0.0030 ** 
## EPA_RegionRegion 6                              0.0144 *  
## EPA_RegionRegion 7                              0.0016 ** 
## EPA_RegionRegion 8                              0.0142 *  
## EPA_RegionRegion 9                              0.0944 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 7.6 on 3904 degrees of freedom
##   (1694 observations deleted due to missingness)
## Multiple R-squared:  0.304,  Adjusted R-squared:   0.3 
## F-statistic: 85.3 on 20 and 3904 DF,  p-value: <0.0000000000000002
##                         GVIF Df GVIF^(1/(2*Df))
## HR_Chal_Index            1.6  1             1.3
## Fin_Tech_Chal_Index      1.7  1             1.3
## Challenge_Customer       1.4  1             1.2
## grouped_owner1           1.5  3             1.1
## grouped_water_source     1.2  2             1.1
## median_income            1.2  1             1.1
## Population_Served_Count  1.3  1             1.1
## NEAR_DIST                1.2  1             1.1
## EPA_Region               1.5  9             1.0

## 
##  Asymptotic one-sample Kolmogorov-Smirnov test
## 
## data:  rz_full_4
## D = 0.06, p-value = 0.000000000000009
## alternative hypothesis: two-sided

Regression tree with additive benefit index

Just trying out a tree to see what mechanisms group suppliers into high or low perception of benefits in general.

Regression tree with additive benefit index with concerns

Added concerns to just see

CART for benefit of each partnership type

Explore level of benefit of each partnership type variables

Data prep

Class tree consolidation

Class tree joint powers

Class tree shared staff

Class tree long term contracting

Class tree short term contracting

Class tree informal

Regression trees for level of benefit of each partnership type

Regression tree consolidation

All splits are challenges, no split based on “control” variables or ownership.

Regression tree joint powers

Regression tree shared staff

Regression tree long-term contracting

Regression tree short term contracting

Regression tree informal

Regression models for each level of benefit for partnership type

Model 5 Consolidation

Model 6 Joint Powers

Model 7 Shared Staff

Model 8 Long-term contracting

Model 9 Short-term contracting

Model 10 Informal

Regression table for models with level of benefit for each type of partnership

Table 4. Regression Results Level of Benefit from Each Partnership Type
Dependent variable:
Level of Benefit for Each Parntership Type Type_of_Partnership_Beneficial_Joint Type_of_Partnership_Beneficial_Shared_Staff_LT Type_of_Partnership_Beneficial_Contracting_LT Type_of_Partnership_Beneficial_Contracting_ST Type_of_Partnership_Beneficial_Informal
Consolidation Joint Powers Shared Staff LT Contracting ST Contracting Informal
(1) (2) (3) (4) (5) (6)
Constant 0.09 0.06 0.41*** 0.50*** 0.47*** 0.66***
(0.09) (0.07) (0.10) (0.12) (0.11) (0.12)
HRChallenge_Managerial_Competence 0.06** 0.06*** 0.05* 0.07* 0.04 0.01
(0.02) (0.02) (0.02) (0.03) (0.03) (0.03)
HRChallenge_Technical_Capabilities 0.05* 0.03+ 0.06** 0.08* 0.10*** 0.13***
(0.02) (0.02) (0.02) (0.03) (0.03) (0.03)
HRChallenge_Manpower 0.09*** 0.04** 0.12*** 0.07** 0.08*** 0.12***
(0.02) (0.02) (0.02) (0.03) (0.02) (0.02)
HRChallenge_Hiring -0.01 -0.001 0.11*** 0.07*** 0.08*** 0.08***
(0.02) (0.01) (0.02) (0.02) (0.02) (0.02)
Challenge_Regulations 0.03 0.01 0.03+ 0.02 0.03 0.05*
(0.02) (0.01) (0.02) (0.02) (0.02) (0.02)
Challenge_Customer 0.07*** 0.04* 0.04* 0.03 0.04 0.05+
(0.02) (0.02) (0.02) (0.03) (0.03) (0.03)
Challenge_Water_Quality 0.08*** 0.04** 0.02 0.07** 0.02 0.01
(0.02) (0.02) (0.02) (0.03) (0.02) (0.02)
grouped_owner1Privately Owned 0.16** 0.10** -0.04 0.08 -0.04 -0.07
(0.05) (0.04) (0.05) (0.07) (0.06) (0.06)
grouped_owner1Community Owned 0.10* 0.02 -0.03 0.04 -0.02 -0.04
(0.05) (0.04) (0.05) (0.06) (0.06) (0.06)
grouped_owner1Other 0.10 0.15+ -0.13 0.21 0.002 -0.17
(0.11) (0.09) (0.12) (0.15) (0.14) (0.14)
grouped_water_sourcePurchased 0.37*** 0.22*** 0.18*** 0.31*** 0.05 0.17**
(0.05) (0.04) (0.05) (0.06) (0.06) (0.06)
grouped_water_sourceSurface water 0.16* 0.03 0.10 0.12 0.11 0.24**
(0.07) (0.05) (0.07) (0.09) (0.08) (0.09)
median_income 0.0000 0.0000 -0.0000 0.0000*** 0.0000*** 0.0000
(0.0000) (0.0000) (0.0000) (0.0000) (0.0000) (0.0000)
Population_Served_Count -0.0000*** -0.0000* -0.0001*** -0.0001*** -0.0000* -0.0000**
(0.0000) (0.0000) (0.0000) (0.0000) (0.0000) (0.0000)
NEAR_DIST -0.0000** -0.0000* -0.0000* -0.0000** -0.0000* -0.0000
(0.0000) (0.0000) (0.0000) (0.0000) (0.0000) (0.0000)
EPA_RegionRegion 10 -0.05 -0.03 -0.14 -0.06 0.01 0.08
(0.08) (0.06) (0.08) (0.11) (0.10) (0.10)
EPA_RegionRegion 2 0.004 0.01 0.04 -0.16 -0.05 0.15
(0.10) (0.08) (0.11) (0.14) (0.13) (0.13)
EPA_RegionRegion 3 0.06 -0.04 -0.04 -0.14 -0.20* -0.12
(0.08) (0.06) (0.08) (0.11) (0.10) (0.10)
EPA_RegionRegion 4 -0.02 -0.09 -0.19* 0.04 0.01 -0.03
(0.08) (0.06) (0.08) (0.11) (0.10) (0.10)
EPA_RegionRegion 5 -0.09 -0.05 -0.07 -0.13 -0.13 -0.05
(0.07) (0.06) (0.07) (0.10) (0.09) (0.09)
EPA_RegionRegion 6 -0.03 -0.11+ -0.19* -0.18+ -0.11 -0.15
(0.08) (0.06) (0.08) (0.10) (0.10) (0.10)
EPA_RegionRegion 7 -0.08 -0.11+ -0.11 -0.21* -0.24* -0.07
(0.08) (0.06) (0.08) (0.10) (0.09) (0.10)
EPA_RegionRegion 8 -0.10 -0.02 -0.02 -0.09 -0.06 -0.13
(0.08) (0.07) (0.09) (0.11) (0.10) (0.11)
EPA_RegionRegion 9 0.13+ 0.02 -0.06 0.02 -0.13 0.05
(0.08) (0.06) (0.08) (0.10) (0.09) (0.10)
Observations 3,937 3,876 3,882 3,902 3,875 3,864
Adjusted R2 0.10 0.06 0.14 0.08 0.09 0.10
Note: (+ p<0.1; * p<0.05; ** p<0.01; *** p<0.001)