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"text": "Yang and Woods",
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"text": "Journal of Food Distribution Research",
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"text": "to sample the products.[p3.3.1] Therefore, the probability of propensity to sample the products can be presented as:",
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"text": "(1)\\ p=pr(y_{i}=1|\\boldsymbol{x}_{i})=F(x^{\\prime}\\boldsymbol{\\beta})=\\left\\{\\begin{matrix}\\frac{\\exp(x_{i}^{\\prime}\\boldsymbol{\\beta})}{1+\\exp(x_{i}^{\\prime}\\boldsymbol{\\beta})}&for~logit\\\\ \\Phi(x_{i}^{\\prime}\\boldsymbol{\\beta})&for~probit\\end{matrix}\\right.",
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"latex": "(1)\\ p=pr(y_{i}=1|\\boldsymbol{x}_{i})=F(x^{\\prime}\\boldsymbol{\\beta})=\\left\\{\\begin{matrix}\\frac{\\exp(x_{i}^{\\prime}\\boldsymbol{\\beta})}{1+\\exp(x_{i}^{\\prime}\\boldsymbol{\\beta})}&for~logit\\\\ \\Phi(x_{i}^{\\prime}\\boldsymbol{\\beta})&for~probit\\end{matrix}\\right.",
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"alt": "1 p equals pr of y sub i equals 1 boldsymbol x sub i equals F of x to the power of prime boldsymbol beta equals begin matrix frac exp of x sub i to the power of prime boldsymbol beta 1 plus exp of x sub i to the power of prime boldsymbol beta &for logit capital phi of x sub i to the power of prime boldsymbol beta &for probit end matrix .",
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"text": "where[p3.5.1] indicates positive propensity to sample;[p3.5.2] denotes independent variables. The probability of the logit model is the cumulative density function of the logistic distribution; and the probability of the probit model is the cumulative density function of the standard normal distribution. The marginal effects are calculated as[p3.5.3] for the logit and probit models. The empirical specifications in this study for pawpaw and sorghum syrup products are:",
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"text": "y_{i}=1",
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"text": "\\text{where } y_i=1 \\text{ indicates positive propensity to sample; } \\boldsymbol{x}_i \\text{ denotes independent variables. The probability of the logit model is the cumulative density function of the logistic distribution; and the probability of the probit model is the cumulative density function of the standard normal distribution. The marginal effects are calculated as } \\partial p/\\partial x_{j}=F'(x'\\beta)\\beta_{j} \\text{ for the logit and probit models. The empirical specifications in this study for pawpaw and sorghum syrup products are:}",
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"latex": "\\text{where } y_i=1 \\text{ indicates positive propensity to sample; } \\boldsymbol{x}_i \\text{ denotes independent variables. The probability of the logit model is the cumulative density function of the logistic distribution; and the probability of the probit model is the cumulative density function of the standard normal distribution. The marginal effects are calculated as } \\partial p/\\partial x_{j}=F'(x'\\beta)\\beta_{j} \\text{ for the logit and probit models. The empirical specifications in this study for pawpaw and sorghum syrup products are:}",
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"notation": "latex",
"alt": "where y sub i equals 1 indicates positive propensity to sample; boldsymbol x sub i denotes independent variables. The probability of the logit model is the cumulative density function of the logistic distribution; and the probability of the probit model is the cumulative density function of the standard normal distribution. The marginal effects are calculated as the partial derivative p over the partial derivative x sub j equals F' x' beta beta sub j for the logit and probit models. The empirical specifications in this study for pawpaw and sorghum syrup products are:",
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"text": "\\begin{array}{rlr}&{}&{(2)~pawpaw=y^{*}=\\beta_{0}+\\beta_{1}X_{1}+\\beta_{2}X_{2}+\\cdots+\\beta_{16}X_{16}+\\varepsilon}\\end{array}",
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"latex": "\\begin{array}{r l r}&{}&{(2)~p a w p a w=y^{*}=\\beta_{0}+\\beta_{1}X_{1}+\\beta_{2}X_{2}+\\cdots+\\beta_{16}X_{16}+\\varepsilon}\\end{array}",
"notation": "latex",
"alt": "begin array rlr & & 2 pawpaw equals y to the power of * equals beta sub 0 plus beta sub 1 X sub 1 plus beta sub 2 X sub 2 plus cdots plus beta sub 16 X sub 16 plus varepsilon end array",
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"text": "(3)~sorghum=y^{*}=\\gamma_{0}+\\gamma_{1}X_{1}+\\gamma_{2}X_{2}+\\cdots+\\gamma_{15}X_{15}+\\varepsilon",
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"latex": "(3)~sorghum=y^{*}=\\gamma_{0}+\\gamma_{1}X_{1}+\\gamma_{2}X_{2}+\\cdots+\\gamma_{15}X_{15}+\\varepsilon",
"notation": "latex",
"alt": "3 sorghum equals y to the power of * equals gamma sub 0 plus gamma sub 1 X sub 1 plus gamma sub 2 X sub 2 plus cdots plus gamma sub 15 X sub 15 plus varepsilon",
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"text": "where the dependent variables (pawpaw and sorghum) are explained by sixteen and fifteen independent variables[p3.8.1], respectively, while the[p3.8.2] and[p3.8.3] are parameters to be estimated. The explanatory variables consist of demographic and regional characteristic variables.",
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"text": "A web-based survey of 3,406 farmers' market patrons was conducted exploring a variety of food sampling questions in eight Mid-South U.S. states (including Virginia, West Virginia, Ohio, Indiana, Illinois, Missouri, Kentucky, and Tennessee) in 2012. The responses of the sample are proportional to the relative population of each state. This survey was conducted through an existing consumer panel maintained by Zoomerang.com, an affiliate of MarketTools, Inc."
},
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"text": "The demographic independent variables included in this study are: Female, Age, Race (white, non-white), Have kids, Education, and Income. Residence was designated as either rural (countryside or farm) or urban (urban or suburban). State location is also identified, i.e. MO, KY, TN, WV, VA, IL, IN, and OH. Ohio is selected to be an intercept state for comparison."
},
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"text": "The definitions and sample descriptive statistics of these variables are presented in Table 1. Over half of the respondents have positive propensity to sample pawpaw and sorghum syrup products."
},
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"order": 19,
"type": "heading",
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"text": "Sampling Interests at Farmers' Markets",
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"text": "Farmers’ markets are popular venues for vendors to introduce unusual and regional products to consumers with an interest shaped by their regional preferences. Pawpaw and sorghum syrup products are popular in the Mid-South of the United States. Respondents were asked how likely they would be to sample a variety of different products if offered during their farmers’ market visit. Individuals responding to pawpaw and sorghum with Likert scores of 6 and 7 (“very"
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"text": "27",
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"text": "[p3.15.1] An ordered logit model was applied first. However, it did not meet the proportional odds assumption (equivalent parameterization), so a generalized ordered logit model, also called partial proportional odds model, was applied. Since the findings of the generalized ordered logit model suggest no particular differences among each group comparison, here we provide the simplest set of outcomes by using binary probit and logit models. The full set of the generalized ordered logit outcomes is available upon request.",
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"text": "²",
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"text": "March 2013",
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},
{
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"text": "Volume 44, Issue 1",
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],
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}