1 Raw data;;;;
;;;;
;NHANES variables;;;
;;;;
;Day1 Name;Day2 Name;Variable Label;
;SEQN;SEQN;Respondent sequence number;
;WTDRD1;WTDRD1;Dietary day one sample weight;
;WTDR2D;WTDR2D;Dietary two-day sample weight;
;DR1ILINE;DR2ILINE;Food/Individual component number;
;DR1DRSTZ;DR2DRSTZ;Dietary recall status;
;DR1EXMER;DR2EXMER;Interviewer ID code;
;DRABF;DRABF;Breast-fed infant (either day);
;DRDINT;DRDINT;Number of days of intake;
;DR1DBIH;DR2DBIH;# of days b/w intake and HH interview;
;DR1DAY;DR2DAY;Intake day of the week;
;DR1LANG;DR2LANG;Language respondent used mostly;
;DR1CCMNM;DR2CCMNM;Combination food number;
;DR1CCMTX;DR2CCMTX;Combination food type;
;DR1_020;DR2_020;Time of eating occasion (HH:MM);
;DR1_030Z;DR2_030Z;Name of eating occasion;
;DR1FS;DR2FS;Source of food;
;DR1_040Z;DR2_040Z;Did you eat this meal at home?;
;DR1IFDCD;DR2IFDCD;USDA food code;
;DR1IGRMS;DR2IGRMS;Grams;
;DR1IKCAL;DR2IKCAL;Energy (kcal);
;DR1IPROT;DR2IPROT;Protein (gm);
;DR1ICARB;DR2ICARB;Carbohydrate (gm);
;DR1ISUGR;DR2ISUGR;Total sugars (gm);
;DR1IFIBE;DR2IFIBE;Dietary fiber (gm);
;DR1ITFAT;DR2ITFAT;Total fat (gm);
;DR1ISFAT;DR2ISFAT;Total saturated fatty acids (gm);
;DR1IMFAT;DR2IMFAT;Total monounsaturated fatty acids (gm);
;DR1IPFAT;DR2IPFAT;Total polyunsaturated fatty acids (gm);
;DR1ICHOL;DR2ICHOL;Cholesterol (mg);
;DR1IATOC;DR2IATOC;Vitamin E as alpha-tocopherol (mg);
;DR1IATOA;DR2IATOA;Added alpha-tocopherol (Vitamin E) (mg);
;DR1IRET;DR2IRET;Retinol (mcg);
;DR1IVARA;DR2IVARA;Vitamin A, RAE (mcg);
;DR1IACAR;DR2IACAR;Alpha-carotene (mcg);
;DR1IBCAR;DR2IBCAR;Beta-carotene (mcg);
;DR1ICRYP;DR2ICRYP;Beta-cryptoxanthin (mcg);
;DR1ILYCO;DR2ILYCO;Lycopene (mcg);
;DR1ILZ;DR2ILZ;Lutein + zeaxanthin (mcg);
;DR1IVB1;DR2IVB1;Thiamin (Vitamin B1) (mg);
;DR1IVB2;DR2IVB2;Riboflavin (Vitamin B2) (mg);
;DR1INIAC;DR2INIAC;Niacin (mg);
;DR1IVB6;DR2IVB6;Vitamin B6 (mg);
;DR1IFOLA;DR2IFOLA;Total folate (mcg);
;DR1IFA;DR2IFA;Folic acid (mcg);
;DR1IFF;DR2IFF;Food folate (mcg);
;DR1IFDFE;DR2IFDFE;Folate, DFE (mcg);
;DR1ICHL;DR2ICHL;Total choline (mg);
;DR1IVB12;DR2IVB12;Vitamin B12 (mcg);
;DR1IB12A;DR2IB12A;Added vitamin B12 (mcg);
;DR1IVC;DR2IVC;Vitamin C (mg);
;DR1IVD;DR2IVD;Vitamin D (D2 + D3) (mcg);
;DR1IVK;DR2IVK;Vitamin K (mcg);
;DR1ICALC;DR2ICALC;Calcium (mg);
;DR1IPHOS;DR2IPHOS;Phosphorus (mg);
;DR1IMAGN;DR2IMAGN;Magnesium (mg);
;DR1IIRON;DR2IIRON;Iron (mg);
;DR1IZINC;DR2IZINC;Zinc (mg);
;DR1ICOPP;DR2ICOPP;Copper (mg);
;DR1ISODI;DR2ISODI;Sodium (mg);
;DR1IPOTA;DR2IPOTA;Potassium (mg);
;DR1ISELE;DR2ISELE;Selenium (mcg);
;DR1ICAFF;DR2ICAFF;Caffeine (mg);
;DR1ITHEO;DR2ITHEO;Theobromine (mg);
;DR1IALCO;DR2IALCO;Alcohol (gm);
;DR1IMOIS;DR2IMOIS;Moisture (gm);
;DR1IS040;DR2IS040;SFA 4:0 (Butanoic) (gm);
;DR1IS060;DR2IS060;SFA 6:0 (Hexanoic) (gm);
;DR1IS080;DR2IS080;SFA 8:0 (Octanoic) (gm);
;DR1IS100;DR2IS100;SFA 10:0 (Decanoic) (gm);
;DR1IS120;DR2IS120;SFA 12:0 (Dodecanoic) (gm);
;DR1IS140;DR2IS140;SFA 14:0 (Tetradecanoic) (gm);
;DR1IS160;DR2IS160;SFA 16:0 (Hexadecanoic) (gm);
;DR1IS180;DR2IS180;SFA 18:0 (Octadecanoic) (gm);
;DR1IM161;DR2IM161;MFA 16:1 (Hexadecenoic) (gm);
;DR1IM181;DR2IM181;MFA 18:1 (Octadecenoic) (gm);
;DR1IM201;DR2IM201;MFA 20:1 (Eicosenoic) (gm);
;DR1IM221;DR2IM221;MFA 22:1 (Docosenoic) (gm);
;DR1IP182;DR2IP182;PFA 18:2 (Octadecadienoic) (gm);
;DR1IP183;DR2IP183;PFA 18:3 (Octadecatrienoic) (gm);
;DR1IP184;DR2IP184;PFA 18:4 (Octadecatetraenoic) (gm);
;DR1IP204;DR2IP204;PFA 20:4 (Eicosatetraenoic) (gm);
;DR1IP205;DR2IP205;PFA 20:5 (Eicosapentaenoic) (gm);
;DR1IP225;DR2IP225;PFA 22:5 (Docosapentaenoic) (gm);
;DR1IP226;DR2IP226;PFA 22:6 (Docosahexaenoic) (gm);
;;;;
;NHANES meals;;;
;;;;
;Code or Value;Value Description;;
;1;Breakfast;;
;2;Lunch;;
;3;Dinner;;
;4;Supper;;
;5;Brunch;;
;6;Snack;;
;7;Drink;;
;8;Infant feeding;;
;9;Extended consumption;;
;10;Desayano;;
;11;Almuerzo;;
;12;Comida;;
;13;Merienda;;
;14;Cena;;
;15;Entre comida;;
;16;Botana;;
;17;Bocadillo;;
;18;Tentempie;;
;19;Bebida;;
;91;Other;;
;99;Don't know;;
;;;;
2 Absorption equations;;;;
;;;;
;  'SF.ug.L ',        # Serum Ferritin in uq/L;;;
;  'VitC.mg',          # Vitamin C in mg;;;
;  'MFP.g',            # Meat, fish, poultry (MFP) in g;;;
;"  'Phytate.mg',       # Phytate in mg (Hallberg; 1 mg phytate = 3.53 mg phytic acid = 5.56 umol phytic acid)";;;
;  'Calcium.mg',       # Calcium in mg;;;
;  'nhIron.mg',        # Non-heme iron in mg;;;
;  'hIron.mg',         # Heme iron in mg;;;
;  'Fruit.Juice.g',    # High-vitamin-C (> 30 mg/100g) fruit or juice in g;;;
;  'Bean.Lentil.g',    # Beans and lentils (exculding soya beans) in g;;;
;  'Cereal.g',         # Wholegrain cereal (e.g. bread, muffins, rice, bran flakes) in g;;;
;  'Tea.g',            # Tea (black tea infusion) in g;;;
;  'Tea.c',            # Tea in cups;;;
;  'Dairy.g',          # Dairy (milk, milk pudding, cream and cottage cheese) in g;;;
;  'Cheese.g',         # Cheese (excluding cream and cottage cheese) in g;;;
;  'Egg.g',            # Eggs in g;;;
;  'Soya.g',           # Soya (beans and flour porridge) in g;;;
;  'Nuts.g',           # Nuts in g;;;
;  'Iron.mg',          # Total amount of iron in mg;;;
;  'Tannic.acid.mg',   # Tannic acid equivalents in mg;;;
;  'MFP.raw.g',        # Meat, poultry, fish and seafood expressed as g of uncooked food. Equivalent of 1g cooked meat = 1.3g raw meat;;;
;  'Alcohol.cons'      # 1: For 1-2 glasses of wine or alcohol beverages per meal. Else 0.;;;
;;;;
;;;;
3 Piecewise linear approximation;;;;
;;;;
;Iron;;;
;;;;
;    c.min.x;;Conway;lowest allowed nutrient value
;    c.segmentsx ;;Conway;x coordinate of line segment
;    c.segmentsy ;;Conway;y coordinate of line segment
;    c.intercept ;;Conway;intercept of first line segment
;    c.slopes ;;Conway;slope of line segment
;    c.distances ;;Conway;horizontal distances between line segments
;    a.min.x ;;Armah;lowest allowed nutrient value
;    a.segmentsx ;;Armah;x coordinate of line segment
;    a.segmentsy ;;Armah;y coordinate of line segment
;    a.intercept ;;Armah;intercept of first line segment
;    a.slopes ;;Armah;slope of line segment
;    a.distances ;;Armah;horizontal distances between line segments
;;;;
;Zinc;;;
;;;;
;equalGridSizePWL;;Whether grid sizes are equal or not;
;percentilePWL;;"Compare accuracy for 2 regions; below and above percentile";
;pctQPWL;;Which percentage of gridpoints should be used for region below percentile. Has no function when gridsize is equal;
;ngridPWL;;Number of grids used (nxn);
;max.zn;;Maximum value grid for zinc;
;max.phy;;Maximum value grid for phytate;
;g.A;;First grid point of triangle;
;g.B;;Second grid point of triangle;
;g.C;;Third grid point of triangle;
;x.A;;X coordinate of first gridpoint;
;x.B;;X coordinate of second gridpoint;
;x.C;;X coordinate of third gridpoint;
;y.A;;Y coordinate of first gridpoint;
;y.B;;Y coordinate of second gridpoint;
;y.C;;Y coordinate of third gridpoint;
;l.A;;Lambda value of first gridpoint;
;l.B;;Lambda value of second gridpoint;
;l.C;;Lambda value of third gridpoint;
;d.x;;Horizontal distance between gridpoints;
;d.y;;Vertical distance between gridpoints;
;d.xy;;Sum of horizontal and vertical distances;
;LU;;Left upper corner of triangle;
;RU1;;First right upper corner of triangle;
;RU2;;Second right upper corner of triangle;
;LB1;;First left bottom corner of triangle;
;LB2;;Second left bottom corner of triangle;
;RB;;Right bottom corner of triangle.;
;Abs.zn.pwl;;Zinc absorption (%) calculated with piecewise linear approximation;
;Abs.zn;;Zinc absorption (%) calculated with nonlinear equation;
;;;;
4 Model input data;;;;
;;;;
;DRV variables;;;
;;;;
;DRV;Dietary reference values;;
;LB;Lower bound on nutrient intake;;
;UB;Upper bound on nutrient intake;;
;EAR;Estimated average requirement;;
;RDA;Recommended daily allowance;;
;UL;Tolerable upper lvel;;
;;;;
;Meal / Consumption variables;;;
;;;;
;"  ""IdentifyingID"",";;;
;"  ""Respondent.sequence.number"",";;;
;"  ""Interview.day"",";;;
;"  ""Time.of.eating.occasion..HH.MM."",";;;
;"  ""Name.of.eating.occasion"",";;;
;"  ""USDA.food.code"",";;;
;"  ""USDA.food.name"",";;;
;"  ""Ingredient"",";;;Simplified name of USDA food name
;"  ""category_description"",";;;WWEIA food subgroup
;"  ""Category"",";;;WWEIA food group
;"  ""Vegetarian"", ";;;Food item / Meal is vegetarian
;"  ""Vegan"", ";;;Food item / Meal is vegan
;"  ""Grams""";;;Amount of reported food intake
;Total.abs.IOM;;;Total iron absorption (%) using IOM's absorption factor
;Total.abs.Constant;;;Total iron absorption (%) using Eustachio's absorption factor
;Total.abs.Hallb;;;Total iron absorption (%) using Hallberg's absorption equation
;Total.abs.Conw;;;Total iron absorption (%) using Conway's absorption equation
;Nh.abs.Hallb.;;;Nonheme iron absorption (%) using Hallberg's absorption equation
;Nh.abs.Conw.;;;Nonheme iron absorption (%) using Conway's absorption equation
;H.abs.Hallb.;;;Heme iron absorption (%) using Hallberg's absorption equation
;h.absorption;;;Heme iron absorption (%) using a constant factor
;Fe.IOM;;;Total iron content (mg) using IOM's absorption factor
;Fe.Constant;;;Total iron content (mg) using Eustachio's absorption factor
;Fe.Hallb;;;Total iron content (mg) using Hallberg's absorption equation
;Fe.Conw;;;Total iron content (mg) using Conway's absorption equation
;nhFe.IOM;;;Nonheme iron content (mg) using IOM's absorption factor
;nhFe.Constant;;;Nonheme iron content (mg) using Eustachio's absorption factor
;nhFe.Hallb;;;Nonheme iron content (mg) using Hallberg's absorption equation
;nhFe.Conw;;;Nonheme iron content (mg) using Conway's absorption equation
;hFe.IOM;;;Heme iron content (mg) using IOM's absorption factor
;hFe.Constant;;;Heme iron content (mg) using Eustachio's absorption factor
;hFe.Hallb;;;Heme iron content (mg) using Hallberg's absorption equation
;hFe.Conw;;;Heme iron content (mg) using Conway's absorption equation
;Zn.mmol;;;Zinc in mmol
;Phy.mmol;;;Phytate in mmol
;;;;
5 Diet models;;;;
;;;;
;PWL;piecewise linear approximation diet model;;
;NLP;nonlinear programming diet model;;
;C 50-40;Continuous model where food item changes were limited to 50% and food group changes to 40%;;
;C 75-50;Continuous model where food item changes were limited to 75% and food group changes to 50%;;
;C 100-60;Continuous model where food item changes were limited to 100% and food group changes to 60%;;
;;;;
;SETS;;;
;n 'Nutrients';;;
;nmacro(n) 'Subset macronutrients';;;
;nmicro(n) 'Subset micronutrients';;;
;nabs(n) 'Subset nutrients affecting iron absorption';;;
;nknown(n) 'Subset nutrients where content is given (all nutrients except absorbable iron)';;;
;r 'Recipes';;;
;i 'Ingredients';;;
;m 'Meal moment';;;
;s_m(m) /'Dinner', 'Lunch'/ ;;;
;g 'Food groups';;;
;z 'PWL zinc' ;;;
;p 'PWL phytate';;;
;;;;
;SCALARS;;;
;NDays 'Number of days to cover by menu plan';;;
;SF 'Serum ferritine';;;
;c /0.001/;;;
;Intercept 'Intercept of piecewise linear approximation';;;
;lnSF 'Natural logarithm of serum ferritin';;;
;ln100 'Natural logarithm of 100';;;
;;;;
;PARAMETERS;;;
;EAR(n) 'Estimated average requirement per day for each micronutrient n';;;
;RDA(n) 'Recommended daily allowance for each micronutrient n';;;
;UL(n) 'Tollerable upper intake level for each micronutrient n';;;
;LB(n) 'Lower bound on intake level for each macronutrient n';;;
;UB(n) 'Upper bound on intake level for each macronutrient n';;;
;fDiversity(i) 'Number of times an ingredient i may be added to the menu plan';;;
;recipeType(r,m) 'Indicates whether recipe r belongs to meal moment m';;;
;recipeIngredients(r,m,i) 'Indicates whether ingredient i belongs to recipe r with meal moment m';;;
;nContent(r,m,n) 'Nutrient n content for each recipe r with meal moment m';;;
;initialSolution(r,m) 'Start solution';;;
;nContentMax(n) 'Maximal nutrient content for all recipes';;;
;slope(s) 'Slope of piecewise linear approximation';;;
;distance(s) 'Distances between breakpoints of piecewise linear approximation';;;
;FgIng(i,g) 'Indicates whether ingredient i belongs to food group g';;;
;obsIntake(i) 'Observed intake (g/day) for ingredient i';;;
;Zn(z) 'PWL zinc in mmol';;;
;Phy(p) 'PWL phytate in mmol';;;
;absZn(z,p) 'PWL absorbable zinc in mmol';;;
;;;;
;INTEGER VARIABLES;;;
;X(r,m) 'Number of times that recipe r is selectded for meal moment m';;;
;;;;
;BINARY VARIABLES;;;
;Y(n,s) 'Needed for delta formulation piecewise linear approximation';;;
;Bul(z,p) 'PWL Binary variable for upper left triangle';;;
;Blr(z,p) 'PWL Binary variable for lower right triangle';;;
;;;;
;POSITIVE VARIABLES;;;
;belowRDA(n) 'Normalised deviation below RDA';;;
;maxBelowRDA 'Maximal deviation below RDA';;;
;hfeAbs 'Estimated heme iron absorption';;;
;nhfeAbs 'Estimated non-heme iron absorption';;;
;absFeIntake 'Absorbable iron intake';;;
;nIntake(r,m,n) 'Nutrient n intake (different units) for selected recipes r for meal moment m';;;
;avgIntake(n) 'Average Nutrient n intake per day';;;
;avgIntakeAdj0(n);;;
;avgIntakeAdj(n) 'Adjusted for iron absorption';;;
;delta(n,s) 'Delta formulation piecewise linear approximation';;;
;lnIntake(n) 'Aproximated natural logarithm of average intake';;;
;X(i) 'Grams of ingredient i';;;
;Qplus(i)  'Positivie quantity change';;;
;Qmin(i)   'Negative quantity change';;;
;Qdiff(i)   'Absolute quantity change';;;
;zn 'Average zinc intake in mmol';;;
;phy 'Average phytate intake in mmol';;;
;absZnIntake 'Average absorbable zinc intake in mg';;;
;znIntake 'Average zinc intake in mmol';;;
;phyIntake 'Average phytate intake in mmol';;;
;lambda(z,p) 'PWL lambda';;;
;;;;
;VARIABLES;;;
;Objective 'Objective function' ;;;