Using Auxiliary Population Samples for Sample-Selection Correction in Models Based on Crowd-Sourced Volunteered Geographic Information

Trudy Ann Cameron; Sonja H. Kolstoe

doi:10.3368/le.98.1.040720-0050R1

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Figure 1
Predicted Probabilities, Engagement Levels 3–6. A: qBus Sample; B: eBird Sample; C: eBird Sample Based on an Ordered-Probit Model Estimated Using the qBus Sample
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Figure 2
Predicted Consideration-Set Radii for 1,081 Observations in the eBird Sample for Models 4 and 5 (in Table 4), Plotted against Predicted Radii from the Naive Model 1
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Figure 3
1,081 eBird Member Survey Observations: Marginal Distribution of Predicted Consideration-Set Radii Using Model1 Overlaid by Selection-Corrected Predictions for (Birders in) the General-Population, Based on Model 5

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Table 1 Descriptive Statistics (Proportions) for Variables in First-Stage Engagement-Intensity Models

	qBus Sample Proportions	eBird Sample Proportions
Engagement data available	1.000	1.000
1=Unfamiliar with eBird CS project	0.802	0.000
2=Heard of eBird but not a member	0.083	0.000
3=eBird member, but report rarely	0.031	0.391
4=eBird member, report <1/2 of birds	0.029	0.280
5=eBird member, report >1/2 of birds	0.030	0.177
6=eBird member, report almost all birds	0.024	0.152
Travel 1+ mile data available	0.442	0.769
Trips 1+ miles = 0	0.348	0.277
Trips 1+ miles = (1,4)	0.063	0.113
Trips 1+ miles = (4,7)	0.065	0.065
Trips 1+ miles = (7,10)	0.048	0.025
Trips 1+ miles = (10,21)	0.076	0.093
Trips 1+ miles = (21,41)	0.065	0.065
Trips 1+ miles = (41,72)	0.063	0.078
Trips 1+ miles = (72,124)	0.065	0.067
Trips 1+ miles = (124,174)	0.063	0.052
Trips 1+ miles = (174,238)	0.063	0.032
Trips 1+ miles = (238,364)	0.062	0.054
Trips 1+ miles = 365	0.017	0.078
Audubon CBC data available	1.000	1.000
Has participated in CBC	0.092	0.528
Bird-hunting data available	1.000	1.000
Hunts birds	0.224	0.073
Gender data available	1.000	0.994
Gender: male	0.489	0.427
Gender: female	0.511	0.573
Age data available	1.000	0.993
Age: ≤24 years	0.125	0.018
Age: 25-34 years	0.224	0.065
Age: 35-44 years	0.196	0.089
Age: 45-54 years	0.135	0.146
Age: 55-64 years	0.175	0.311
Age: ≥65 years	0.145	0.370
Income data available	1.000	0.804
Income: <$25K	0.179	0.072
Income: $25K-$50K	0.219	0.203
Income: $50K-$75K	0.189	0.231
Income: $75K-$100K	0.141	0.173
Income: ≥$100K	0.272	0.321
Region data available	1.000	1.000
Region: West	0.225	1.000
Region: Northeast	0.186	0.000
Region: Midwest	0.217	0.000
Region: South	0.372	0.000
Employment status data available	1.000	0.849
Employment status: full time	0.473	0.359
Employment status: part time	0.132	0.080
Employment status: looking for work	0.057	0.008
Employment status: unemployed	0.145	0.066
Employment status: retired	0.193	0.487
Education data available	1.000	0.976
Education: high school	0.226	0.036
Education: some college	0.356	0.158
Education: college grad	0.263	0.288
Education: master’s degree	0.118	0.396
Education: doctoral degree	0.038	0.121
Observations	4,161	1,081

Note: Availability indicators are proportions of the total sample; group shares are proportions of the available data.

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Table 2 Estimated Coefficients, Ordered-Probit Engagement-Level Models Examples with Maximum Heterogeneity

	Ordered Probit qBus Data		Ordered Probit eBird Data
Travel 1+mile data available	0.136	(0.661)	_—^a
Trips 1+miles = 0	−0.870	(0.667)	−2.828^***	(0.228)
Trips 1+miles = [1,4)	−0.260	(0.678)	−3.113^***	(0.268)
Trips 1+miles = [4,7)	−0.554	(0.683)	−1.862^***	(0.287)
Trips 1+miles = [7,10)	−0.388	(0.681)	−2.243^***	(0.372)
Trips 1+miles = [10,21)	−0.0566	(0.667)	−1.820^***	(0.250)
Trips 1+miles = [21,41)	−0.0189	(0.668)	−1.496^***	(0.262)
Trips 1+miles = [41,72)	0.287	(0.665)	−1.354^***	(0.254)
Trips 1+miles = [72,124)	0.518	(0.663)	−0.711^***	(0.258)
Trips 1+miles = [124,174)	0.400	(0.663)	−0.644^**	(0.293)
Trips 1+miles = [174,238)	0.487	(0.662)	−0.582^*	(0.321)
Trips 1+miles = [238,364)	0.730	(0.661)	−0.422	(0.286)
Trips 1+miles = 365	0.699	(0.687)	_—^b
Has participated in CBC	1.916^***	(0.0706)	0.170	(0.107)
Hunts birds	0.0640	(0.0965)	−0.0767	(0.181)
Gender: female	−0.169^***	(0.0509)	−0.111	(0.107)
Relative to Omitted Category: 45-54 years
Age: ≤24 years	0.539^***	(0.0991)	0.994^**	(0.424)
Age: 25-34 years	0.545^***	(0.0871)	0.293	(0.216)
Age: 35-44 years	0.360^***	(0.0894)	0.325^*	(0.192)
Age: 55-64 years	−0.207^*	(0.110)	−0.117	(0.159)
Age: ≥65 years	−0.298^**	(0.134)	0.146	(0.201)
Relative to Omitted Category: $50K-$75K
Income: <$25K	−0.0590	(0.0853)	−0.0751	(0.254)
Income: $25K-$50K	−0.0192	(0.0774)	0.143	(0.150)
Income: $75K-$100K	−0.0423	(0.0867)	−0.0150	(0.158)
Income: ≥$100K	−0.0118	(0.0784)	0.143	(0.138)
Relative to Omitted Category: West
Region: Northeast	0.164^**	(0.0737)	_—^b
Region: Midwest	−0.0186	(0.0754)	_—^b
Region: South	0.0552	(0.0660)	_—^b
Relative to Omitted Category: Full Time
Empl. status: part time	0.0409	(0.0751)	−0.148	(0.188)
Empl. status: looking for work	−0.173	(0.108)	−0.819	(0.650)
Empl. status: unemployed	−0.109	(0.0805)	−0.0110	(0.217)
Empl. status: retired	−0.148	(0.107)	−0.325^**	(0.163)
Relative to Omitted category: 4-Year College Degree
Education: high school	−0.0294	(0.0754)	0.693^**	(0.309)
Education: some college	−0.128^*	(0.0671)	0.00246	(0.170)
Education: master’s degree	0.269^***	(0.0826)	0.259^**	(0.121)
Education: doctoral degree	0.165	(0.124)	0.00792	(0.165)
Ordered-Probit Thresholds
Cut1	1.279^***	(0.113)	−2.651^***	(0.288)
Cut2	1.895^***	(0.116)	−1.309^***	(0.279)
Cut3	2.258^***	(0.119)	−0.363	(0.274)
Cut4	2.690^***	(0.123)	_—^c
Cut5	3.341^***	(0.132)	_—^c
Observations		4,161		572
Max. log likelihood		−2,390.32		−582.44

Note:The first model is a six-level model using the full qBus sample. The second is a four-level model for the subset of 572 eBird survey respondents with complete data for this least-restricted specification. Specifications with fewer explanatory variables can use more observations in the eBird data set. Other models to accommodate all of the patterns of missing variables in the eBird data are in the Appendixes.
↵a Too few missing values to identify this coefficient.
↵b These indicators are zero for all observations in the eBird data.
↵c There are only four levels of engagement in the eBird data.
↵* p < 0.05;
↵** p < 0.01;
↵*** p < 0.001.

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Table 3 Descriptive Statistics

	Mean	Std. Dev.
Dependent Variable (Consideration-Set-Radius, Lower Bound of Chosen Interval)
Self-reported maximum radius (i.e., extent) of travel in miles	83.28	58.10
Explanatory Variable
Employment status: employed	0.373	0.484
Income data available	0.804	0.397
Income in 10k, if reported	7.011	5.891
Gender: female	0.570	0.495
Age: <45 years	0.171	0.377
Age: >64 years	0.367	0.482
Education: graduate school	0.505	0.500
No interest: perching birds	0.057	0.233
No interest: other game birds	0.111	0.314
Selection-Correction Options
Binary-probit IMR	2.035	1.212
Adjusted ordered probit IMR	1.668	0.978
Engagement propensity (demeaned using qBus mean)	0.657	1.261
Observations	1,081

Note: Variables are for the outcome model, elicited from the eBird member survey sample for n = 1,081 respondents who answered the question about maximum one-way distance for a birding day trip.

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Table 4 Consideration-Set-Radius Models without and with Engagement-Intensity Weights and Either Sample-Selection Corrections or Interactions between All Regressors and Demeaned Ordered-Probit Selection Propensities

	(1)	(2)	(3)	(4)	(5)
Model	Naive	Weights Only	Binary Probit IMR	Ordered Probit IMR	Demeaned Propensity
Main Variable
Empl. Status: employed	−0.0351 (0.0696)	−0.0613 (0.0973)	−0.0872 (0.0943)	−0.0934 (0.0936)	−0.299^* (0.154)
Income data available	−0.429^*** (0.127)	−0.362** (0.180)	−0.342* (0.176)	−0.354^** (0.175)	−0.223 (0.186)
ln(Income in 10K, if reported)	0.218^*** (0.0533)	0.171^** (0.0730)	0.156^** (0.0718)	0.158^** (0.0710)	0.0628 (0.0887)
Gender: female	−0.127^** (0.0590)	−0.123 (0.0796)	−0.0374 (0.0787)	−0.0410 (0.0783)	0.000944 (0.106)
Age: <45 years	0.185^** (0.0835)	0.225^** (0.112)	0.167 (0.106)	0.137 (0.108)	−0.317 (0.197)
Age: >64 years	−0.0489 (0.0713)	−0.114 (0.0982)	−0.0287 (0.100)	−0.103 (0.0961)	−0.0110 (0.115)
Education: graduate school	0.113^* (0.0598)	0.0132 (0.0751)	−0.0649 (0.0741)	−0.0642 (0.0748)	−0.259^*** (0.0958)
No interest: perching birds	−0.811^*** (0.148)	−0.862^*** (0.198)	−0.847^*** (0.205)	−0.829^*** (0.202)	−0.749^*** (0.190)
No interest: other game birds	−0.634^*** (0.107)	−0.660^*** (0.130)	−0.577^*** (0.131)	−0.578^*** (0.130)	−0.549^*** (0.127)
Constant	4.066^*** (0.0972)	4.170^*** (0.127)	4.494^*** (0.135)	4.403^*** (0.131)	4.102^*** (0.140)
Selection-Correction Strategy
Binary-probit IMR			−0.169^*** (0.0305)
Ordered probit IMR				−0.386^*** (0.0689)
Interaction between Main Variables and Demeaned Engagement Propensity (Demeaned Using qBus Sample Mean)
Empl. Status: employed × engagement prop. (demeaned)					0.185 (0.158)
Income data avail. × engagement prop. (demeaned)					−0.120 (00756)
ln(Income in 10K, if reported) × engagement prop. (demeaned)					0.134^* (0.0692)
Gender: female × engagement prop. (demeaned)					0.224^* (0.117)
Age: <45 years × engagement prop. (demeaned)					−0.00451 (0.0733)
Age: >64 years × engagement prop. (demeaned)					−0.0223 (0.0607)
Education: graduate school × engagement prop. (demeaned)					0.0176 (0.0551)
No interest: perching birds × engagement prop. (demeaned)					−0.231 (0.175)
No interest: other game birds × engagement prop. (demeaned)					0.160 (0.107)
Constant × engagement prop. (demeaned)					0.282^*** (0.0813)
ln(σ_ε)	−0.0803^*** (0.0237)	−0.0583^* (0.0306)	−0.0788^** (0.0313)	−0.0808^*** (0.0310)	−0.105^*** (0.0310)
Observations	1,081	1,081	1,081	1,081	1,081
Log likelihood	−2,411.41	−2,429.96	−2,409.82	−2,408.03	−2,382.37
AIC	4,844.83	4,881.92	4,843.64	4,840.05	4,806.74
BIC	4,899.67	4,936.77	4,903.47	4,899.88	4,911.44
Weighted?	No	Yes	Yes	Yes	Yes

Note: Standard errors are in parentheses. Dependent variable: log of maximum one-way distance willingly traveled on a typical birdwatching day trip.
↵* p< 0.05;
↵** p< 0.01;
↵*** p< 0.001.