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Comments on anthropometry, nutritional status, and energy intake
M. Mahmud Khan
Food Research Institute, Stanford University, Stanford, Calif., USA
In a recent article in Food and Nutrition Bulletin , Hassan and Ahmad tried to estimate relationships between nutritional status measured by anthropometry and the nutrient intake of children. The correlation and regression analysis that the authors used indicated a close relationship between these variables. Unfortunately, the model is specified in a way that captures the underlying relationship between the co-variate of age and anthropometry rather than the causal link between calorie consumption and its impact on anthropometric measurements of nutrition.
The authors started their analysis by looking into the correlation co-efficient between the anthropometric measurements and the calorie intake of different age groups. Information about the individuals within the age range 1-19 years was used to estimate log-linear regression equations. However, pooling the data of children of different ages for estimating a bi-variate regression with calorie intake as the independent variable and an anthropometric measure as the dependent variable results in an upward bias of the estimated co-efficient if age and calorie intake are positively correlated, which they obviously are (see Yotopoulos and Nugent  for a discussion on the omitted-variable bias). The problem created by the omission of the age variable is shown in figure 1, in which cluster A represents observations for a lower age group and cluster B those for higher ages. A least-squares regression estimates an equation like L, while the true relationship is something like La for A and Lb for B.
Examination of the group-specific data and some of the reported correlations also indicates that the authors basically estimated the effect of age. For example, consider the anthropometric measurements and calorie intake of the age group 1-3 years, reported in table 1 of the article. Due to the rapid growth of the children in that age range, the categories of lower calorie intake are expected to be dominated by younger children, while older children are more likely to be in the categories of higher calorie intake. A comparison of anthropometric measurements of the lowest- and highest-calorie intake categories within the age group with those of children at the boundary ages of the age group indicates the validity of the above conjecture, Because of the lack of data on Bangladesh, we will use the mean height and weight of Guatemalan Ladino children at ages 12 and 36 months 15]. The weight and height for the lowest-calorie category are 70.3 cm and 7.7 kg, respectively, while the measurements for Guatemalan children at the age of 12 months are 69.2 cm and 7.9 kg. Also, the mean anthropometry for the highest-calorie category and for the children at age 36 months is very close89.1 cm and 11.9 kg for the highest-calorie category and 86.5 cm and 12.17 kg for 36-month-old Guatemalan children. The conclusion is that even within an age group the correlation co-efficient is, to a great extent, influenced by the ages of the children.
Consider also the correlation co-efficients between the skinfold thickness and calorie intake reported in the paper. A positive correlation is reported for the age group 1-3 years and a negative correlation for age 4-6 years. It is well known that skinfold thickness shows irregular patterns with age .
Fig. 1. Illustration of the problem created when the age variable is omitted
Table 1 reproduces the triceps and biceps skinfold thickness at ages 12-72 months for Guatemalan children . Note that the measurement shows an increasing trend in the age range 12-36 months and a declining trend in the range 42-72 months. Therefore the correlation co-efficients between the variables age and skinfold thickness for the Guatemalan children of the two age groups will be exactly the same as those obtained by Hassan and Ahmad.
RE-ESTIMATING THE IMPACT OF ENERGY INTAKE
Two alternative approaches can be adopted for the proper specification of the regression model. First, one can convert the anthropometric measures into an index of nutritional status that is independent of the age of children. Waterlow et al.  suggested using standard deviation scores of height-forage and weight-for-height as indicators of nutritional status. Second, if the age groups have narrow age ranges, one can introduce age-group-specific dummy variables to allow the shifting of the equations.
The re-estimation is carried out in this section by using the second approach with the groups data reported in tables 1 to 5 in that article. It should be noted that the age range selected for grouping the data is very large (see Waterlow et al.  for recommended age groups for the presentation of anthropometric data), and therefore the estimates obtained below are not free from the omitted-variables bias explained above. For our estimation, the mid-value of each class of calorie intake was considered the mean calorie intake, while for open class intervals the differences between the means of the nearest classes were used to estimate the mean from the lower or the upper boundary of the classes. Since class means are used rather than individual data, the regression results are expected to differ from the results reported in the table 6 of Waterlow et al.'s article. The re-estimated coefficients of their table 6 using the grouped data are reported in table 2.
Note that the co-efficients are comparable to those obtained by Hassan and Ahmad. Our R2 is higher, however, and this is not unlikely when grouped data are used. Since our data are age-group specific, the best one can do is to control for the age groups. This is done by incorporating age-group dummies in the equations. This approach assumes that the effect of calories on any one anthropometric measure is similar for all age groups, but the function shifts upward as one moves from a lower to a higher age group. The results are reported in table 3. The contribution of calories on the nutritional indices becomes less than half when the age group dummies are introduced. Clearly, the effects of energy intake on the anthropometric measures were overestimated by the authors, while the omission of the age-controlling variable led to an overestimate of the co-efficients by more than 100 per cent.
TABLE 1. Skinfold thickness in rural Guatemalan Ladino children (mm)
|Age in months||Boys||Girls|
Source: Malina et al. [2, tables 1 and 2].
TABLE 2. Relationship between calorie intake and some anthropometric measurements (log-linear relationship) in rural Guatemalan Ladino childrena
|Log of the measure||Constant (a)||Co-efficient (b)||R2|
a. For children of age 1-19
b. Figures in parentheses indicate the standard errors of estimation.
TABLE 3. Relationship between calorie intake and some anthropometric measurements (logarithm) after controlling for the age groups in rural Guatemalan Ladino children
a. C-1 to C-5 are the intercept terms for the age groups 1-3 years, 4-6 years, 10-19-year-old male, and 10- 19-year-old female respectively.
The discussion suggests that age should be included as a co-variate in the analysis since it is an underlying variable for both nutritional and anthropometric measurements. It should also be noted that the effect of energy intake on various anthropometric measurements is expected to differ from one age group to another (table 14 of Valverde et al.  indicates differential impact of energy on anthropometry with age). Therefore, the variable-co-efficient model may be more appropriate than the ordinary least-squares formulations.
When short-period nutrition survey data are used, controlling the age of the children may not be sufficient. The initial weight of children of the same age may differ and part of the variability in calorie intake can be explained by the weight factor. The positive relationship between the calorie intake and anthropometric measurements in such a case indicates merely that bigger children ate more during the survey period.
The author is grateful to Professors Reynaldo Martorell and Pan Yotopoulos for comments on an earlier draft.
1. N. Hassan and K. Ahmad, "Anthropometry and Nutritional Status as a Function of Energy Intake in Children 0 to 19 Years Old in Bangladesh," Food and Nutrition Bulletin, 6131: 44 ( 1984).
2. R. M. Malina, J.-P. Habicht, C. Yarbrough, H. Martorell, and R. E Klein, "Skinfold Thickness at Seven Sites in Rural Guatemalan Ladino Children: Birth through Seven Years of Age," Human Biology, 46(3): 453 (1974).
3.V. Valverde, H. Delgado, R. Martorell, J. Belizan, E. Ramirez, v. M. Pivaral, and R. E, Klein, "The Measurement of Individuals, Food Intake in Longitudinal Nutritional Studies in Poor Rural Communities in Guatemala," Monograph 14, Division of Human Development (Institute of Nutrition of Central America and Panama (INCAP), Guatemala City, 1980).
4. J. C. Waterlow, R. Buzina, W. Keller, J. M, Lane, M. Z. Nichaman, and J. M. Tanner, "The Presentation and Use of Height and Weight Data for Comparing the Nutritional Status of Groups of Children under the Age of 10 Years," Bulletin of the World Hearth Organization, 55(4): 489 (1977).
5. C. Yarbrough, J.-P. Habicht, R. M, Malina, A. Lechtig, and R. E. Klein, "Length and Weight in Rural Guatemalan Ladino Children: Birth to Seven Years of Age," American Journal of Physical Anthropology, 42(3): 439 ( 1975).
6. P. Yotopoulos and J. Nugent, Economics of Development: Empirical Investigations (Harper & Row, New York, 1976).
The reviewer's comments on this article may be of interest to the reader.
The problem called attention to by Mr. Khan is a common pitfall in the interpretation of regression co-efficients as indicators of change in a dependent variable associated with changes in the corresponding regression variables. That this is not necessarily the case is illustrated by the drastic changes frequently observed in the estimates of regression co-efficients according to what other variables are included in the model. Such changes can be expected whenever there is co-linearity among the regression variables, that is, when their values tend to be correlated in the sampled data. In this connection, the exclusion of variables may also alter the regression estimates where the included variables, at least in part, serve as proxies for effects of excluded variables. Mr. Khan's article illustrates this point.
Mosteller and Tukey  provide a good discussion of the general problems of co-linearity, and Mandel  and Mansfield and Helms , among others, have described some practical approaches for detecting and managing co linearity and near co-linearity in regression analysis. At present, however, there is no definitive solution for this fundamental problem of regression models.
Dr. Miguel A. Guzmán
Department of Pathology
Louisiana State University Medical School
New Orleans, La., USA
1. F. Mosteller and J. W. Tukey, Data Analysis and Regression: A Second Course in Statistics (Addison-Wesley, Reading, Mass., 1977).
2. J. Mandel, "Use of the Singular Value Decomposition in Regression Analysis," Am. Star., 36: 15-24 (1982)
3. E R. Mansfield and B. P. Helms, "Detecting Multicolinearity," Am. Stat, 36: 158-169 (1982).
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