Data

NHANES is an ongoing nationally representative survey of the noninstitutionalized civilian resident population in the 50 states and the District of Columbia of the United States. The survey uses multiyear sampling strategies and publishes the data every two years. In addition to information on individuals’ health and nutrition status, the survey includes a dietary intake module known as What We Eat in America (WWEIA). Individuals participating in this module complete two 24-hour dietary recalls on nonconsecutive days. They recall a detailed description of each food and beverage consumed and the consumption amounts. This information can be further matched with an individual's age, ethnicity (race), household income, education, and other demographic characteristics as captured in the broader NHANES.

Multiple cycles of NHANES were used to estimate the model conditional on the covariates shown in Table 1. The covariates assumed to influence diets were the following: log of age, age squared, log of years in the U.S., log of individual income, and indicator variables for marital status, gender, education, and ethnicity. Our data sample consists of adults from 20 to 80 years of age. Table 1 shows that the average (weighted) age is 42.94 years. To construct an income variable which is comparable between households of different size in different years the following procedure was used: The original survey question consisted of 15 different intervals of household income. First, we set household income to the midpoint value of each interval. Then, for each individual, we divided the household income by the square root of the number of people in the household (OECD 2008). Finally, the income variable was deflated by the national consumer price index for the survey year. The income variable may then be interpreted as (an index of) the log of real individual income. Further, in our data, 64 percent are married, 48 percent are male, 18 percent have less than high school education, 24 percent has finished high school, and 58 percent has college education. Eighty-five percent of our sample was born in the United States.

Table 1. Summary Statistics

Note: Included participants are 20 years or older. The mean and the standard errors are weighted with the NHANES sampling weights.

Each year about 5,000 individuals participated in the NHANES. A total of 30,667 respondents who were 20 years or older were included to estimate the association between ethnicity and diets using seven cycles from the NHANES surveys: 1999–2000, 2001–2002, 2003–2004, 2005–2006, 2007–2008, 2009–2010, and 2011–2012. More details of the NHANES database are described in the National Center for Health Statistics (2013).

Histograms (Figure 1) of daily per capita consumption of milk, meat, processed meat, fruits, and vegetables show that, in our data, large shares of respondents did not consume each of the food types on the days of the survey, i.e., there are mixtures of two distributions: one for the consumed quantities of a food and another for non-consumption of the food. In addition, all the histograms are skewed to the right. This indicates that the daily food consumption is censored gamma distributed. From Table 1 we note that 85 percent of our sample was born in the United States, and the largest group born in the U.S. is whites. The largest immigrant group is Hispanics, comprising about 8 percent of the sample.

Figure 1. Histograms of Daily per Capita Consumption

The (weighted) shares of respondents who consumed the different food groups on a daily basis are shown in Table 2. About half the U.S.-born (51 percent) drank milk every day, while 56 percent of the immigrants did so. More people born in the U.S. (81 percent) than immigrants (75 percent) consumed meat every day. The consumption rate of processed meat was also higher among U.S.-born people (45 percent) than immigrants (40 percent). The rates were lowest among Hispanic immigrants (36 percent) and black immigrants (40 percent). A larger share of immigrants (74 percent) than U.S.-born (62 percent) consumed fruits every day. The rate of daily vegetable consumption of all respondents was between 82 percent and 89 percent.

Table 2. Share of Respondents who Consumed the Food Groups on a Daily Basis

Note: The standard deviations are printed in the parentheses. The mean and the standard deviations are weighted with the NHANES sampling weights. These weights incorporate adjustments for unequal selection probability, non-responses, and corrections for age, sex, and ethnicity categories.

There were also many substantial differences in the consumption between U.S.-born and immigrants for many ethnic groups. For example, the rate of daily consumption of milk was 17 percentage points higher among blacks immigrants than among blacks born in the U.S., daily meat consumption was 13 percentage points higher among blacks born in the U.S. than among black immigrants, daily processed meat consumption was 11 percentage points higher among Hispanics born in the U.S. than among Hispanic immigrants, and daily fruit consumption was 18 percentage points higher among Asian immigrants than Asians born in the U.S. Such differences indicate that several immigrant groups are at risk of getting a less healthy diet.

The daily (weighted) average consumption of each food category by each ethnic group is shown in Table 3. The consumption of milk was higher among U.S.-born (144 grams) than immigrants (132 grams). U.S.-born whites had the highest milk consumption (157 grams), while U.S.-born blacks had the lowest (70 grams). Meat consumption was also higher among U.S.-born (93 grams) than immigrants (82 grams). blacks born in the U.S. had the highest consumption (120 grams), while Asian immigrants consumed the least (62 grams). Immigrants consumed less processed meat (76 grams) than U.S.-born (86 grams). However, Asian immigrants had the highest consumption of processed meat (92 grams), while Hispanic immigrants had the lowest (66 grams). Fruit consumption was substantially higher among immigrants (192 grams) than U.S.-born (132 grams). White immigrants consumed more than twice as much fruit (234 grams) as Hispanics born in the U.S. (113 grams). The consumption of vegetables was also higher among immigrants (155 grams) than U.S.-born (134 grams). White immigrants had the highest vegetable consumption (173 grams), while blacks (107 grams) and Asians (108 grams) born in the U.S. had the lowest consumption.

Table 3. Daily Average Consumption of Food Groups Across Ethnic Groups

Note: Consumption is measured in grams. The standard deviations are printed in the parentheses. The mean and the standard deviations are weighted with the NHANES sampling weights. These weights incorporate adjustments for unequal selection probability, non-responses, and corrections for age, sex, and ethnicity categories.

Several immigrant groups seem to be at risk of getting a less healthy diet after some time of residency in the U.S. For example, the consumption of milk was 34 grams higher among black immigrants than among blacks born in the U.S., meat consumption was 39 grams higher among blacks born in the U.S. than among black immigrants, processed meat consumption was 23 grams higher among Hispanics born in the U.S. than among Hispanic immigrants, fruit consumption was 100 grams higher among white immigrants than whites born in the U.S., and vegetable consumption was 32 grams higher among white immigrants than among whites born in the U.S.

Econometric Model

For each food group, we estimated the probability of consumption and the daily consumption. As discussed above, the distribution of the daily consumption of each food group is skewed to the right and censored at zero. Hence, the daily consumption of each group is not normally distributed, and the use of Tobit type censored regression models could produce inconsistent results (Pagan and Vella Reference Pagan and Vella1989; Lee Reference Lee1996). Consequently, we estimated a generalized linear model with a zero-adjusted gamma distribution (Rigby and Stasinopoulos Reference Rigby and Stasinopoulos2005; Tong, Mues, and Thomas Reference Tong, Mues and Thomas2013). The gamma distribution is part of the exponential family of probability distributions, which typically are used to construct generalized linear models (GLM).Footnote ¹

Our response variable, y is assumed to follow a gamma distribution when it is positive. The gamma distribution is given by:

(1)$$f\lpar y\semicolon \;\beta \comma \;\alpha \rpar = \left[{\displaystyle{1 \over {\Gamma \lpar \alpha \rpar \beta^\alpha }}} \right]y^{\alpha -1}e^{{-}y/\beta }\comma \;$$

where the parameters α > 0 and β > 0, and Γ(α) is the gamma function. The mean of y is given by:

(2)$$E\lpar y\rpar = \mu = \alpha \beta \comma \;$$

and the variance of y is given by:

(3)$${\mathop{\rm var}} y = \sigma ^2 = \alpha \beta ^2.$$

Equations (1), (2), and (3) are used to reparametrize the gamma distribution to be a function of μ and σ ², such that:

(4)$$f\lpar y\vert \mu \comma \;\sigma \rpar = \left[{\displaystyle{1 \over {{\lpar \sigma^2\mu \rpar }^{1/\sigma^2}}}} \right]\left[{\displaystyle{{y^{1/\sigma^2-1}e^{{-}y/\lpar \sigma^2\mu \rpar }} \over {\Gamma \lpar 1/\sigma^2\rpar }}} \right]. $$

We assume a log link function, which ensures non-negative predictions:

(5)$$\eta _1 = \log \lpar \mu \rpar = {x}^{\prime}_1\beta _1\comma \;$$

where ${x}^{\prime}_1\beta _1$ is the linear predictor in the gamma regression model.

To take account of the censoring in our data, we include a probability term, π, defined as the cumulative of a logistic distribution:

(6)$$ { \it π} = \displaystyle{{e^{{{x}^{\prime}}_{\!\!2}\beta _2}} \over {1 + e^{{{x}^{\prime}_2}\beta _2}}}.$$

For 0 ≤ y < ∞ the model is given by:

(7)$$f\lpar y\vert \mu \comma \;\sigma \comma \;\mu \rpar = \left\{\matrix{{\it &#x03C0;} \,\,{\rm if}\,\,y = 0 \hfill \cr \lpar 1 - {\it &#x03C0;} \rpar \left[{\displaystyle{1 \over {{\lpar \sigma^2\mu \rpar }^{1/\sigma^2}}}\displaystyle{{y^{1/\sigma^2-1}e^{{-}y/\lpar \sigma^2\mu \rpar }} \over {\Gamma \lpar 1/\sigma^2\rpar }}} \right]\quad {\rm if}\;y \gt 0 \hfill} \right.\,.\,\,$$

Equations (5) to (7) are the GLM model with the zero adjusted gamma (ZAGA) distribution. The associated likelihood function is given by:

(8)$$L = \prod\limits_{y = 0} {\it &#x03C0;} \prod\limits_{y \gt 0} {\lpar 1 - {\it &#x03C0;} \rpar \left[{\displaystyle{1 \over {{\lpar \sigma^2\mu \rpar }^{1/\sigma^2}}}\displaystyle{{y^{1/\sigma^2-1}e^{{-}y/\lpar \sigma^2\mu \rpar }} \over {\Gamma \lpar 1/\sigma^2\rpar }}} \right]} .$$

The conditional expectation of the outcome variable of Equation (2) becomes:

(9)$$E\lpar y\vert x_1\comma \;x_2\rpar = \left[{1-\displaystyle{{e^{{{x}^{\prime}\!}_2\beta_2}} \over {1 + e^{{{x}^{\prime}\!}_2\beta_2}}}} \right]e^{{{x}^{\prime}}_ {\! 1}\beta _1}.$$

To investigate the effects of time of stay since immigration to the U.S, we calculate the expected difference in probability and consumption level between an immigrant who has been in the U.S. for less than a year, and an immigrant who has been in the U.S. for five years. We chose a five-year time span given that this would generally be considered enough amount of time to adjust to the U.S. food culture. Let $\hat{{\it &#x03C0;} }_{ij5} = \lsqb {1-{\hat{{\it &#x03C0;} }}_{ij}\lpar {{\bar{x}}^{\prime}}_{\! 2}{\hat{\beta }}_2\vert {\rm time}\, = 5\;{\rm years}\rpar } \rsqb$ and $\hat{{\it &#x03C0;} }_{ij1} = \lsqb {1-{\hat{{\it &#x03C0;} }}_{ij}\lpar {{\bar{x}}^{\prime}}_ {\! 2}{\hat{\beta }}_2\vert {\rm time}\;\lt 1\,{\rm year}\rpar } \rsqb$. Then, for each food and ethnic group, we calculate the difference in the predicted probability, $\Delta \hat{{\it &#x03C0;} }$, and consumption level, $\Delta \hat{\mu }$, as:

(10)$$\Delta \hat{{\it &#x03C0;} }_{ij} = \lpar 1-\hat{{\it &#x03C0;} }_{ij5}\rpar -\lpar 1-\hat{{\it &#x03C0;} }_{ij1}\rpar = \hat{{\it &#x03C0;} }_{ij1}-\hat{{\it &#x03C0;} }_{ij5}$$

and

(11)$$\eqalign{& \Delta {\hat{\mu }}_{ij} = \displaystyle{{\lsqb \lpar 1-{\hat{{\it &#x03C0;} }}_{ij5}\rpar \exp \lpar {{\bar{x}}^{\prime}}_{\! 1}{\hat{\beta }}_1\vert {\rm time} = 5\,{\rm years}\rpar -\lpar 1-{\hat{{\it &#x03C0;} }}_{ij1}\rpar \exp \lpar {{\bar{x}}^{\prime}}_{\! 1}{\hat{\beta }}_1\vert {\rm time}\,\lt 1\,{\rm year}\rpar \rsqb \cdot 100} \over {\lpar 1-{\hat{{\it &#x03C0;} }}_{ij1}\rpar \exp \lpar {{\bar{x}}^{\prime}}_{\! 1}{\hat{\beta }}_1\vert {\rm time}\,\lt 1\,{\rm year}\rpar }}\comma \;\cr & } $$

where $\bar{x}_1\;{\rm and}\;\bar{x}_2$are the vectors of mean values of the regressors in Equations (5) and (6) and the ethnic dummy variables are set to either zero or one.

The model was estimated by using the covariates in Table 1 and the R package GAMLSS. To calculate the standard errors, we used a nonparametric bootstrap. In each bootstrap repetition, the probability of positive consumption and consumption level were predicted. This procedure was repeated 500 times, and the covariance matrix between the predictions was used to create the standard errors and t-statistics of the expected probabilities and consumption levels.