Introduction: Nutritional deprivation has increasingly emerged as a critical dimension of welfare inequality, particularly in developing countries where economic, social, and spatial vulnerabilities intersect to shape patterns of dietary inadequacy. In Iran, this issue has become more prominent as rural households face mounting pressures from rising food prices, declining purchasing power, and structural shifts in consumption behavior. At the same time, widening regional disparities have made equitable access to diverse and nutrient-rich foods more challenging. Conventional food security assessments often rely on calorie-based or expenditure-based metrics, which although useful for estimating basic food sufficiency, fail to capture qualitative aspects of nutrient intake and frequently overlook hidden forms of deprivation that persist even when caloric needs are met. Many rural diets may be calorie-adequate but deficient in essential micronutrients such as vitamins, minerals, and proteins, resulting in long-term health and welfare consequences. These limitations underscore the need for multidimensional and region-specific approaches that provide deeper insights into nutritional inequality. In this context, the present study introduced a multidimensional Nutritional Deprivation Index (NDI) tailored to rural Iran. By integrating both macronutrient and micronutrient indicators and applying a data-driven weighting method, the study aimed at delivering a more comprehensive understanding of nutritional deprivation and its spatial distribution across provinces of the country.
Materials and Methods: This study adopted a multidimensional framework to evaluate nutritional deprivation among rural households. The NDI is constructed using indicators representing the consumption of key macronutrients (including protein and total caloric intake) and essential micronutrients such as vitamins A and C, iron, and calcium. Nutrient intake data were derived from nationally representative rural household consumption surveys, ensuring provincial comparability. To determine the relative importance of each indicator, the entropy method was employed. This technique assigns higher weights to indicators with greater inter-provincial variation, capturing significant differences in nutritional patterns and avoiding subjective weighting biases. Following the calculation of NDI scores, the Jenks Natural Breaks classification method was used to group the provinces into five deprivation categories including very low, low, medium, high, and very high deprivations. The Jenks algorithm identifies natural groupings by minimizing inter-class variance and maximizing intra-class variance, producing a more accurate and interpretable spatial categorization. The integration of multidimensional indexing, entropy weighting, and spatial classification provided a robust methodological foundation for assessing the nutritional deprivation in rural Iran. 
Results and Discussion: The study findings indicated that micronutrient deficiencies would exert a substantial influence on overall nutritional deprivation. Entropy weights highlighted protein, vitamins A and C, iron, and calcium as the most influential contributors to inter-provincial variation, indicating the importance of diet quality. Thus, even when caloric intake was sufficient, widespread deficiencies in essential nutrients persisted, revealing the limitations of calorie-centered assessments. The NDI scores ranging from 0.09 to 0.82 indicated pronounced heterogeneities across the provinces. The results of West Azerbaijan (0.09), Hormozgan (0.22), Sistan and Baluchestan (0.23), Guilan (0.25), and Hamadan (0.27) provinces fell into the “very high deprivation” category, which might reflect economic constraints, limited access to diverse foods, agricultural limitations, and supply chain inefficiencies; in contrast, the results of Chaharmahal and Bakhtiari (0.79) and South Khorasan (0.82) provinces showed their category of “very low deprivation”, which might be attributed to more diverse agricultural production, cultural dietary habits, or stronger regional food systems. Notably, several economically advanced and highly urbanized provinces including Razavi Khorasan, Tehran, East Azerbaijan, Isfahan, and Kerman appeared in the “medium deprivation” or “high deprivation” categories. This pattern suggested that the concerned nutritional deprivation was not determined solely by economic capacity or agricultural production, but also associated with consumption patterns, diet quality, and access to micronutrients. This pattern indicated that nutritional challenges persisted even in wealthier regions, potentially due to increased consumption of processed foods, lifestyle changes, and market fluctuations affecting access to nutrient-dense foods. These findings underscored that the nutritional deprivation in rural Iran was shaped by complex socioeconomic and geographic factors and could not be explained solely by poverty or calorie deficits. These findings pointed to the presence of “hidden nutritional deprivation”, where adequate caloric intake might coexist with insufficient micronutrient consumption.
Conclusion and Suggestions: The study concluded that the nutritional deprivation among rural households in Iran was inherently multidimensional and could not be accurately assessed through single-indicator measures. By incorporating both macro- and micronutrient indicators and applying entropy-based weighting, the NDI offered a more nuanced and reliable depiction of deprivation and its spatial disparities. Therefore, the policy recommendations of the study may include some measures as follows: prioritizing access to essential micronutrients (particularly, protein, vitamins A and C, iron, and calcium) within national nutrition and rural development initiatives; strengthening food distribution systems to ensure affordability and stability; and improving nutritional literacy through community-based education efforts. Finally, the pronounced regional disparities identified in the analysis highlighted the need for targeted, province-specific strategies rather than uniform nationwide policies, while integrating nutritional education, agricultural diversification, local food system support, and improved distribution networks would be critical for reducing deprivation and promoting long-term rural wellbeing.