nutritional_adequacy.org

Preface

import cfe
import matplotlib.pyplot as plt

r = cfe.result.from_dataset('Indian ICRISAT.ds')
UseNutrients=['Protein','Calories','Iron']

Nutritional requirements

Individuals have nutritional requirements established by nutrition scientists. Here are some standards established by the Indian National Institute of Nutrition:

Nutritional needs of individuals

Recommended Daily Allowances: India

Sex-Age	Calories	Protein	Fat	Calcium	Iron	Betacarotene	Thiamine	Riboflavin	Niacin	Ascorbic Acid
C 0-0.5				500			.2	.3		25
C 0.5-1			19	500	5	2800	.3	.4		25
C 1-3	1060	16.7	27	600	9	3200	.5	.6	8	40
C 4-6	1350	20.1	25	600	13	3200	.7	.8	11	40
C 7-9	1690	29.5	30	600	16	4800	.8	1.	13	40
B 10-12	2190	39.9	35	800	21	4800	1.1	1.3	15	40
G 10-12	2010	40.4	35	800	27	4800	1.	1.2	13	40
B 13-15	2750	54.3	45	800	32	4800	1.4	1.6	16	40
G 13-15	2330	51.9	40	800	27	4800	1.2	1.4	14	40
B 16-17	3020	61.5	50	800	28	4800	1.5	1.8	17	40
G 16-17	2440	55.5	35	800	26	4800	1.	1.2	14	40
M	2730	60	30	600	17	4800	1.4	1.4	18	40
W	2230	55	25	1200	21	4800	1.1	1.3	14	40

Recommended Daily Allowances: Tanzania

Sex-Age	Calories	Protein	Vitamin A	Vitamin B6	Vitamin B12	Vitamin C	Vitamin D	Vitamin E	Calcium	Iron	Magnesium	Zinc
C 0-2	680	13.05	395833	0.35	0.725	28.75	5	3850	437.5	4.325	51.25	3.775
C 2-5	900	13.8	400000	0.55	1.05	30	5	5000	550	5.05	68	4.45
C 6-9	1260	19.581875	400000	0.9	1.65	33.75	5	6500	675	6.875	94	5.4
C 10-14	1650	31.4712	400000	1.35	2.43	38.5	5	8400	840	9.22	128	6.65
C 15-17	2020	42.126	400000	1.67	3	41.67	5	9670	966.67	10.867	153.33	7.6
Men	2800	45.8344	600000	1.5	2.4	45	5	10000	1150	9	260	7
Women	2290	45.8344	500000	1.4	2.4	45	5	5000	1150	20	220	4.9

Nutritional Needs of Households

Our data on demand and nutrients is at the household level; we can’t directly compare household level nutrition with individual level requirements. What we can do is add up minimum individual requirements, and see whether household total exceed these. This isn’t a guarantee that all individuals have adequate nutrition (since the way food is allocated in the household might be quite unequal, or unrelated to individual requirements), but it is necessary if all individuals are to have adequate nutrition.

For the average household in the ICRISAT villages, the number of different kinds of people can be computed by averaging over households:

# In first round, averaged over households and villages

zbar = r.z.sel(t=r.firstround,drop=True).mean(['j','m'])[:-1].squeeze() # Leave out log HSize

zbar = zbar.to_dataframe().squeeze()

Now, the inner/dot/matrix product between zbar and the rda DataFrame of requirements will give us minimum requirements for the average household:

rda = pd.read_pickle('indian_rda.df').T

# May need to tweak types to match RDA and zbar types:
zbar['C 0-3'] = zbar['M 0-3'] + zbar['F 0-3']
zbar['C 4-8'] = zbar['M 4-8'] + zbar['F 4-8']
zbar['M'] = zbar['M 19-30'] + zbar['M 31-50'] + zbar['M 51+']
zbar['F'] = zbar['F 19-30'] + zbar['F 31-50'] + zbar['F 51+']
zbar = zbar[['C 0-3','C 4-8','M 9-13','F 9-13','M 14-18','F 14-18','M','F']]

rda['C 0-3'] = rda['C 0-0.5'] + rda['C 0.5-1'] + rda['C 1-3']
rda['C 4-8'] = rda['C 4-6'] + rda['C 7-9']
rda['M 9-13'] = rda['B 10-12']
rda['F 9-13'] = rda['G 10-12']
rda['M 14-18'] = rda['B 13-15'] + rda['B 16-17']
rda['F 14-18'] = rda['G 13-15'] + rda['G 16-17']
rda['F'] = rda['W']

rda = rda[['C 0-3','C 4-8','M 9-13','F 9-13','M 14-18','F 14-18','M','F']]

# This matrix product gives minimum nutrient requirements for average
# household in 1975
hh_rda = rda.replace('',0).T@zbar
hh_rda

Nutritional Adequacy of Food Demands

Since we can trace out demands for nutrients as a function of $(x,p)$, and we’ve computed minimum nutritional requirements for the average household, we can normalize nutritional intake to check the adequacy of diet.

def nutrient_adequacy_ratio(x,pscale=None):
    return nutrient_demand(x,pscale=pscale)/hh_rda

In terms of normalized nutrients, any household with more than one unit of any given nutrient (or zero in logs) will be consuming a minimally adequate level of the nutrient; below this level there’s clearly nutritional inadequacy. For this reason the ratio of actual nutrients to required nutrients is termed the “nutrient adequacy ratio,” or NAR.

plt.plot(X,pd.concat({x:np.log(nutrient_adequacy_ratio(x,p))[UseNutrients] for x in X},axis=1).T)
plt.legend(UseNutrients)
plt.xlabel('log budget')
plt.ylabel('log nutrient adequacy ratio')
plt.axhline(0)

As before, we can also vary relative prices. Here we trace out nutritional adequacy varying the price of a single good:

poorer_x = x/2

plt.plot(pd.concat({p0:np.log(nutrient_adequacy_ratio(poorer_x,my_prices(p0,i=USE_GOOD)))[UseNutrients] for p0 in P},axis=1).T,P)
plt.legend(UseNutrients)
plt.ylabel('Price')
plt.xlabel('log nutrient adequacy ratio')
plt.axvline(0)
plt.axhline(p.sel(i=USE_GOOD).values)