access to fast-food outlets is linked to a rise in obesity (Powell et al. 2009; Larson et al. 2011; Currie et al. 2010). FAFH tends to be more calorie dense than foods prepared at home. Most consumers may be unaware of the high levels of calories, fat, saturated fat, and sodium found in many menu items and may underestimate actual calorie content (Burton et al. 2006). In particular, low-income and minority neighborhoods have disproportionately lower levels of access to healthier food sources and greater access to less healthy food sources (i.e. food deserts) (Bridle-Fitzpatrick 2015; Gibson 2011). Studies find significant associations between food environment, FAFH and weight gain (for example, see Kim et al. 2014; Seguin et al. 2016; Zeng and Zeng 2018).

Despite the growth of the literature on the effects of the food environment and FAFH, there are still significant research gaps (Steeves et al. 2014). In particular, a more detailed assessment of the food environment with regard to the (micro) nutritional quality of FAFH and the interplay of FAFH and excess body weight is needed for the design of better food environment interventions. The unique data set of this study includes micronutrients of most-consumed meals from a representative restaurant survey allowing us to shed light on this relationship at the population level in urban Peru. Among the different nutrients, we can identify the main drivers of poor nutritional quality and which combination of micronutrients are most likely to contribute to excess body weight when consumed above the recommended intake.

The present study differs from the current literature in three important ways. First, instead of using dietary recall data provided by interviewees on the frequency and quality of FAFH, which is prone to substantial measurement error, the study relies on detailed objective _nutritional information_ on the most frequently _consumed menus_ in the food environment of individuals. The detailed nutritional information is supplied by a representative sample of 1,605 restaurants in the Lima Metropolitan Area, among which nutrition professionals and experts at the National Institute of Statistics and Informatics collected information on the main menus offered. For each restaurant, nutritional specialists observed the preparation of the most popular menu and recorded and weighted all ingredients. In addition, for a subset of restaurants, the ingredients were taken to the laboratory for further analysis. As a result, we can calculate exact, objective data on the quantity of calories, proteins, fat, carbohydrates, fiber, zinc, iron, beta carotene, vitamin A1, vitamin A, vitamin C and sodium. There appears to be no comparable restaurant study in the developing world.<sup>2</sup> Second, to make the best use of these nutritional data and to overcome the limitations of current diet quality indicators, we propose a novel index called _Proportional Difference of Relative Nutrient Intake_ (PDRNI) index. This index computes the relative difference between the _real intake of nutrients per menu_ and the _recommended intake_ . The focus is on the restricted nutrients (fat, carbohydrates and sodium) that are most likely to contribute to body overweight if consumed above the recommended intake (Scheidt and Daniel 2004).

Third, in contrast to smaller-scale studies, we can assess the links among nutritional

> 2 The trade-off of having such detailed information at the restaurant level comes from not having individual-level consumption data.

3