Recreation Demand Data

Description

Cross-section data on the number of recreational boating trips to Lake Somerville, Texas, in 1980, based on a survey administered to 2,000 registered leisure boat owners in 23 counties in eastern Texas.

Usage

data("RecreationDemand")

Format

A data frame containing 659 observations on 8 variables.

trips

Number of recreational boating trips.

quality

Facility's subjective quality ranking on a scale of 1 to 5.

ski

factor. Was the individual engaged in water-skiing at the lake?

income

Annual household income of the respondent (in 1,000 USD).

userfee

factor. Did the individual pay an annual user fee at Lake Somerville?

costC

Expenditure when visiting Lake Conroe (in USD).

costS

Expenditure when visiting Lake Somerville (in USD).

costH

Expenditure when visiting Lake Houston (in USD).

Details

According to the original source (Seller, Stoll and Chavas, 1985, p. 168), the quality rating is on a scale from 1 to 5 and gives 0 for those who had not visited the lake. This explains the remarkably low mean for this variable, but also suggests that its treatment in various more recent publications is far from ideal. For consistency with other sources we handle the variable as a numerical variable, including the zeros.

Source

Journal of Business & Economic Statistics Data Archive.

http://www.amstat.org/publications/jbes/upload/index.cfm?fuseaction=ViewArticles&pub=JBES&issue=96-4-OCT

References

Cameron, A.C. and Trivedi, P.K. (1998). Regression Analysis of Count Data. Cambridge: Cambridge University Press.

Gurmu, S. and Trivedi, P.K. (1996). Excess Zeros in Count Models for Recreational Trips. Journal of Business & Economic Statistics, 14, 469–477.

Ozuna, T. and Gomez, I.A. (1995). Specification and Testing of Count Data Recreation Demand Functions. Empirical Economics, 20, 543–550.

Seller, C., Stoll, J.R. and Chavas, J.-P. (1985). Validation of Empirical Measures of Welfare Change: A Comparison of Nonmarket Techniques. Land Economics, 61, 156–175.

See Also

CameronTrivedi1998

Examples

data("RecreationDemand")

## Poisson model:
## Cameron and Trivedi (1998), Table 6.11
## Ozuna and Gomez (1995), Table 2, col. 3
fm_pois <- glm(trips ~ ., data = RecreationDemand, family = poisson)
summary(fm_pois)
logLik(fm_pois)
coeftest(fm_pois, vcov = sandwich)

## Negbin model:
## Cameron and Trivedi (1998), Table 6.11
## Ozuna and Gomez (1995), Table 2, col. 5
library("MASS")
fm_nb <- glm.nb(trips ~ ., data = RecreationDemand)
coeftest(fm_nb, vcov = vcovOPG)

## ZIP model:
## Cameron and Trivedi (1998), Table 6.11
library("pscl")
fm_zip <- zeroinfl(trips ~  . | quality + income, data = RecreationDemand)
summary(fm_zip)

## Hurdle models
## Cameron and Trivedi (1998), Table 6.13
## poisson-poisson
fm_hp <- hurdle(trips ~ ., data = RecreationDemand, dist = "poisson", zero = "poisson")
## negbin-negbin
fm_hnb <- hurdle(trips ~ ., data = RecreationDemand, dist = "negbin", zero = "negbin")
## binom-negbin == geo-negbin
fm_hgnb <- hurdle(trips ~ ., data = RecreationDemand, dist = "negbin")

## Note: quasi-complete separation
with(RecreationDemand, table(trips > 0, userfee))

Results

R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
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> library(AER)
Loading required package: car
Loading required package: lmtest
Loading required package: zoo

Attaching package: 'zoo'

The following objects are masked from 'package:base':

    as.Date, as.Date.numeric

Loading required package: sandwich
Loading required package: survival
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/AER/RecreationDemand.Rd_%03d_medium.png", width=480, height=480)
> ### Name: RecreationDemand
> ### Title: Recreation Demand Data
> ### Aliases: RecreationDemand
> ### Keywords: datasets
> 
> ### ** Examples
> 
> data("RecreationDemand")
> 
> ## Poisson model:
> ## Cameron and Trivedi (1998), Table 6.11
> ## Ozuna and Gomez (1995), Table 2, col. 3
> fm_pois <- glm(trips ~ ., data = RecreationDemand, family = poisson)
> summary(fm_pois)

Call:
glm(formula = trips ~ ., family = poisson, data = RecreationDemand)

Deviance Residuals: 
     Min        1Q    Median        3Q       Max  
-11.8465   -1.1411   -0.8896   -0.4780   18.6071  

Coefficients:
             Estimate Std. Error z value Pr(>|z|)    
(Intercept)  0.264993   0.093722   2.827  0.00469 ** 
quality      0.471726   0.017091  27.602  < 2e-16 ***
skiyes       0.418214   0.057190   7.313 2.62e-13 ***
income      -0.111323   0.019588  -5.683 1.32e-08 ***
userfeeyes   0.898165   0.078985  11.371  < 2e-16 ***
costC       -0.003430   0.003118  -1.100  0.27131    
costS       -0.042536   0.001670 -25.467  < 2e-16 ***
costH        0.036134   0.002710  13.335  < 2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for poisson family taken to be 1)

    Null deviance: 4849.7  on 658  degrees of freedom
Residual deviance: 2305.8  on 651  degrees of freedom
AIC: 3074.9

Number of Fisher Scoring iterations: 7

> logLik(fm_pois)
'log Lik.' -1529.431 (df=8)
> coeftest(fm_pois, vcov = sandwich)

z test of coefficients:

              Estimate Std. Error z value  Pr(>|z|)    
(Intercept)  0.2649934  0.4324810  0.6127 0.5400559    
quality      0.4717259  0.0488508  9.6565 < 2.2e-16 ***
skiyes       0.4182137  0.1938713  2.1572 0.0309922 *  
income      -0.1113232  0.0503083 -2.2128 0.0269101 *  
userfeeyes   0.8981653  0.2469086  3.6376 0.0002751 ***
costC       -0.0034297  0.0146973 -0.2334 0.8154852    
costS       -0.0425364  0.0117348 -3.6248 0.0002892 ***
costH        0.0361336  0.0093860  3.8497 0.0001183 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

> 
> ## Negbin model:
> ## Cameron and Trivedi (1998), Table 6.11
> ## Ozuna and Gomez (1995), Table 2, col. 5
> library("MASS")
> fm_nb <- glm.nb(trips ~ ., data = RecreationDemand)
> coeftest(fm_nb, vcov = vcovOPG)

z test of coefficients:

              Estimate Std. Error  z value  Pr(>|z|)    
(Intercept) -1.1219363  0.1909098  -5.8768 4.183e-09 ***
quality      0.7219990  0.0399627  18.0668 < 2.2e-16 ***
skiyes       0.6121388  0.1395255   4.3873 1.148e-05 ***
income      -0.0260588  0.0401183  -0.6495     0.516    
userfeeyes   0.6691676  0.4488554   1.4908     0.136    
costC        0.0480087  0.0103573   4.6353 3.565e-06 ***
costS       -0.0926910  0.0060193 -15.3990 < 2.2e-16 ***
costH        0.0388357  0.0087604   4.4331 9.288e-06 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

> 
> ## ZIP model:
> ## Cameron and Trivedi (1998), Table 6.11
> library("pscl")
Loading required package: lattice
Classes and Methods for R developed in the

Political Science Computational Laboratory

Department of Political Science

Stanford University

Simon Jackman

hurdle and zeroinfl functions by Achim Zeileis

> fm_zip <- zeroinfl(trips ~  . | quality + income, data = RecreationDemand)
> summary(fm_zip)

Call:
zeroinfl(formula = trips ~ . | quality + income, data = RecreationDemand)

Pearson residuals:
    Min      1Q  Median      3Q     Max 
-6.3255 -0.2714 -0.1809 -0.1646 13.3126 

Count model coefficients (poisson with log link):
             Estimate Std. Error z value Pr(>|z|)    
(Intercept)  2.099163   0.111397  18.844  < 2e-16 ***
quality      0.033833   0.023914   1.415    0.157    
skiyes       0.471691   0.058187   8.106 5.21e-16 ***
income      -0.099780   0.020779  -4.802 1.57e-06 ***
userfeeyes   0.610488   0.079435   7.685 1.53e-14 ***
costC        0.002369   0.003818   0.620    0.535    
costS       -0.037600   0.002038 -18.454  < 2e-16 ***
costH        0.025234   0.003355   7.522 5.40e-14 ***

Zero-inflation model coefficients (binomial with logit link):
            Estimate Std. Error z value Pr(>|z|)    
(Intercept)  3.29191    0.51608   6.379 1.79e-10 ***
quality     -1.91407    0.20619  -9.283  < 2e-16 ***
income      -0.04502    0.10797  -0.417    0.677    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Number of iterations in BFGS optimization: 23 
Log-likelihood: -1181 on 11 Df
> 
> ## Hurdle models
> ## Cameron and Trivedi (1998), Table 6.13
> ## poisson-poisson
> fm_hp <- hurdle(trips ~ ., data = RecreationDemand, dist = "poisson", zero = "poisson")
> ## negbin-negbin
> fm_hnb <- hurdle(trips ~ ., data = RecreationDemand, dist = "negbin", zero = "negbin")
> ## binom-negbin == geo-negbin
> fm_hgnb <- hurdle(trips ~ ., data = RecreationDemand, dist = "negbin")
> 
> ## Note: quasi-complete separation
> with(RecreationDemand, table(trips > 0, userfee))
       userfee
         no yes
  FALSE 417   0
  TRUE  229  13
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>