**3.2.2 General geoadditive structural model**

$$
\omega\_i = u\_i' \alpha + f\_1(\mathbf{x}\_{i1}) + \dots + f(\mathbf{x}\_{iq}) + f\_{\mathcal{S}^{\text{av}}}(\mathbf{s}\_i) + \delta\_{i'} \tag{5}
$$

with independent and identically distributed Gaussian errors ~ (0,1) *<sup>i</sup> N* . The restriction to =var( )=1 is necessary for identifiability reasons.

**RESULTS.** We applied a geoadditive latent variable model, using the three types of undernutrition as indicators of latent nutritional status. The decision which covariates should be used in the measurement model, and which should be used in the structural equation, is based on the same criteria that was used in (Khatab 2007; Khatab and Fahrmeir 2009).

Associations Between Nutritional Indicators Using Geoadditive

Latent Variable Models with Application to Child Malnutrition in Nigeria 551

other indicators. According to the covariate of radio, it has mostly a non-significant effect. Moreover, the results of LVM2 indicate a negative effect of the education on the indicator 2.

**Parameter Mean Std 2.5% 10% 90% 97.5% Factor Loadings** stunting λ11 \*\* 1.041 0.021 1.00 1.02 1.079 1.095 underweight λ21 \*\* 1.191 0.007 1.178 1.187 1.208 1.210 Wasting λ<sup>31</sup> \*\* 0.673 0.017 0.644 0.656 0.703 0.714 **Parametric indirect Effects** urban -0.057 0.049 -0.153 -0.119 0.011 0.044 anvis 0.054 0.065 -0.058 -0.013 0.153 0.198 toilet \*\* 0.142 0.059 0.017 0.060 0.212 0.250 elect \* 0.0683 0.056 -0.026 0.010 0.151 0.186 **Parametric Direct Effects** male <sup>11</sup> ( ) *a* \*\* 0.238 0.0518 -0.321 -0.285 -0.153 -0.119 work <sup>12</sup> ( ) *a* 0.09 0.055 -0.042 -0.007 0.134 0.168 trepr <sup>13</sup> ( ) *a* \* 0.155 0.069 -0.004 0.041 0.226 0.274 water <sup>14</sup> ( ) *a* \*\* 0.083 0.035 0.0148 0.0384 0.127 0.153 educ <sup>15</sup> ( ) *a* \*\* 0.216 0.039 0.143 0.167 0.265 0.291 radio <sup>16</sup> ( ) *a* 0.062 0.0300 -0.029 -0.0095 0.0711 0.093 male <sup>21</sup> ( ) *a* \*\* 0.064 0.0138 -0.082 -0.067 -0.032 -0.030 work <sup>22</sup> ( ) *a* \*\* 0.109 0.0176 0.051 0.056 0.085 0.107 trepr <sup>23</sup> ( ) *a* \*\* 0.072 0.023 0.024 0.026 0.085 0.117 water <sup>24</sup> ( ) *a* \*\* 0.048 0.007 0.039 0.043 0.057 0.065 educ 25 ( ) *a* \*\* 0.067 0.013 0.0507 0.058 0.074 0.076 radio <sup>26</sup> ( ) *a* \*\* 0.047 0.0056 0.004 0.005 0.020 0.039 male <sup>31</sup> ( ) *a* \* 0.051 0.042 -0.015 0.010 0.119 0.148 work <sup>32</sup> ( ) *a* \* 0.096 0.0453 -0.006 0.021 0.135 0.163 trepr <sup>33</sup> ( ) *a* -0.056 0.056 -0.182 -0.141 0.005 0.045 water 34 ( ) *a* 0.001 0.028 -0.054 -0.036 0.037 0.056 educ 35 ( ) *a* \*\* 0.076 0.032 -0.135 -0.115 -0.035 -0.015 radio <sup>36</sup> ( ) *a* 0.0018 0.0248 -0.068 -0.050 0.013 0.032 **Smoothing Parameters** Chage \*\* 0.035 0.028 0.008 0.01 0.065 0.107 BMI \*\* 0.004 0.0056 0.0006 0.001 0.010 0.018 Mageb \*\* 0.003 0.0045 0.0004 0.0006 0.007 0.015 reg \*\* 0.121 0.045 0.055 0.071 0.175 0.227

Table 3. Results of LVM2, including direct and indirect effects. (\*\*: Statistically significant at

The reason for this is that in the analysis of latent models, we used three indicators (which were assumed to have high level of correlations among each other) instead of one indicator,

2.5% and 10%)

which was used by the separate analysis.

Our interest is in analyzing the three types of undernutrition of children using latent variable models, and in investigating how they can be established as indicators of the latent variable ''undernutrition status''. Based on the previous separate analyses (Khatab, 2007), we are able to determine which factors can have direct effects and which can have indirect effects on the indicators.

In order to choose the covariates used in the measurement model (which have direct effects on the disease indicators); or in the case of the structural model, those have indirect effects via their common impact on the latent variable "nutritional status," we used the following criteria: if the effects of covariates turned out to be significantly different (in terms of confidence intervals) for the three diseases, we decided to keep them in the measurement model, otherwise covariates were included in the geoadditive predictor of the structural equation for the latent variable (Khatab and Fahrmeir 2009).

We started by using the easiest model possible, a classic factor analysis for continuous indicators. The predictor of the structural equation of the model yields LMV0:

$$
\eta = 0 \tag{6}
$$

Estimates of factor loadings are depicted in Table 2. The estimated mean factor loadings show that indicator 2 (*weight-for-age*) has the highest factor loading. That means the most effect on the z-scores is on underweight for age and is followed by the indicator of stunting.

The classic factor analysis model has been extended by introducing direct and indirect parametric covariates, which modified the latent construct.


Table 2. Results of Model LVM0 of Z-scores indicators with = 0 .

The next model was selected based on the previous separate analyses (reported in Khatab, 2007). This leads to the latent variable model.

In the fundamental analysis (LVM1), the vector *<sup>j</sup> a* comprises the covariates urban, antenatal visits, educational level of mothers, access to flush toilet, and availability of electricity, with direct effects on *<sup>j</sup> y* ; and *ui* comprises the remaining categorical covariates sex, work, treatment during pregnancy and access to controlled water and radio, having common effects on the latent variable . However, the results of model LVM1 (not reported here) have been extended or changed to model LVM2 by including some covariates that have direct effects on the parametric direct covariates in LVM2. The results of model LVM2 (Table 3) shows that most of the parametric direct covariates are significant and remained quite stable when including these covariates in the direct parametric effects. It demonstrates that the female children whose mothers are educated, had treatment during their pregnancy, had access to controlled water, had access to radio and working currently have higher Z-score of *weight-for-age* and are better nourished. However, males whose mothers are currently working are associated with a higher level of *(weight-for-height)*(at 97%). Although working status has a slight effect on the indicator of stunting, it is associated with

Our interest is in analyzing the three types of undernutrition of children using latent variable models, and in investigating how they can be established as indicators of the latent variable ''undernutrition status''. Based on the previous separate analyses (Khatab, 2007), we are able to determine which factors can have direct effects and which can have indirect

In order to choose the covariates used in the measurement model (which have direct effects on the disease indicators); or in the case of the structural model, those have indirect effects via their common impact on the latent variable "nutritional status," we used the following criteria: if the effects of covariates turned out to be significantly different (in terms of confidence intervals) for the three diseases, we decided to keep them in the measurement model, otherwise covariates were included in the geoadditive predictor of the structural

We started by using the easiest model possible, a classic factor analysis for continuous

Estimates of factor loadings are depicted in Table 2. The estimated mean factor loadings show that indicator 2 (*weight-for-age*) has the highest factor loading. That means the most effect on the z-scores is on underweight for age and is followed by the indicator of stunting. The classic factor analysis model has been extended by introducing direct and indirect

**Parameter Mean Std 2.5% 97.5% Factor Loadings** 

<sup>11</sup> 1.244 0.02 1.206 1.28

<sup>31</sup> 0.770 0.015 0.739 0.801

The next model was selected based on the previous separate analyses (reported in Khatab,

In the fundamental analysis (LVM1), the vector *<sup>j</sup> a* comprises the covariates urban, antenatal visits, educational level of mothers, access to flush toilet, and availability of

sex, work, treatment during pregnancy and access to controlled water and radio, having

here) have been extended or changed to model LVM2 by including some covariates that have direct effects on the parametric direct covariates in LVM2. The results of model LVM2 (Table 3) shows that most of the parametric direct covariates are significant and remained quite stable when including these covariates in the direct parametric effects. It demonstrates that the female children whose mothers are educated, had treatment during their pregnancy, had access to controlled water, had access to radio and working currently have higher Z-score of *weight-for-age* and are better nourished. However, males whose mothers are currently working are associated with a higher level of *(weight-for-height)*(at 97%). Although working status has a slight effect on the indicator of stunting, it is associated with

<sup>21</sup> 1.36 0.08 1.353 1.38

.

comprises the remaining categorical covariates

. However, the results of model LVM1 (not reported

= 0 (6)

indicators. The predictor of the structural equation of the model yields LMV0:

equation for the latent variable (Khatab and Fahrmeir 2009).

parametric covariates, which modified the latent construct.

Table 2. Results of Model LVM0 of Z-scores indicators with = 0

effects on the indicators.

1. stunting

3. wasting

2. underweight

2007). This leads to the latent variable model.

electricity, with direct effects on *<sup>j</sup> y* ; and *ui*

common effects on the latent variable


other indicators. According to the covariate of radio, it has mostly a non-significant effect. Moreover, the results of LVM2 indicate a negative effect of the education on the indicator 2.

Table 3. Results of LVM2, including direct and indirect effects. (\*\*: Statistically significant at 2.5% and 10%)

The reason for this is that in the analysis of latent models, we used three indicators (which were assumed to have high level of correlations among each other) instead of one indicator, which was used by the separate analysis.

Associations Between Nutritional Indicators Using Geoadditive

nutritionally vulnerable for children in Nigeria.

Latent Variable Models with Application to Child Malnutrition in Nigeria 553

remainder of the third year. This pattern highlights the first two years of life as the most

Fig. 1. Nonlinear effects from top to bottom: child's age, mother's BMI and mother's age at birth for LVM1 (left) and LVM2 (right) of "malnutrition status" of children for Nigeria,

The nonlinear effect of the BMI of the mother shows that obesity of the mother probably poses less of a risk for the child's nutritional status, due to the fact that a very low BMI suggested acute undernutrition of the mother. The Z-score is highest (and thus stunting

using latent varaible model for continuous responses

lowest) at a BMI of around 30-40 months.

It is observed that the indicators have a higher correlation which can affect the results, so we have made a further analysis excluding the indicator of wasting (*weight-for-hight*) to examine the effects of various factors on the other indicators (underweight and stunting), and results are compared (LVM3) with analysis when all three indicators (LVM2) are present.

The results of LVM3 (Table 4) indicate that the antenatal visits and the availability of electricity are associated positively with nutritional status. With regard to the direct covariates, the females and the education level of mothers have a positive significant effect on the indicator of stunting. While, only the work status is associated positively with the indicator of underweight. The factor loadings estimates show that the *weight-for-height* is seen to be more serious in Nigeria (its higher factor loading of 1.14).


Table 4. Estimates of factor loadings of the LVM3 with only two indicators in Niegria.

Figure 1 shows the non-linear effect of the child's age to be associated with a malnutrition status in Nigeria for LVM1 and LVM2, respectively. It shows that the rates of malnutrition of children increase sharply from about 5 to around 20 months of age. The rates of malnutrition are at low level between 20 and 30 months of age, then rise again through the

It is observed that the indicators have a higher correlation which can affect the results, so we have made a further analysis excluding the indicator of wasting (*weight-for-hight*) to examine the effects of various factors on the other indicators (underweight and stunting), and results

The results of LVM3 (Table 4) indicate that the antenatal visits and the availability of electricity are associated positively with nutritional status. With regard to the direct covariates, the females and the education level of mothers have a positive significant effect on the indicator of stunting. While, only the work status is associated positively with the indicator of underweight. The factor loadings estimates show that the *weight-for-height* is

**Parameter Mean Std 2.5% 97.5% Factor Loadongs**

**Parametric Indirect Effects**

**Parametric Direct Effects**

**Smoothing Parameters**

 Chage \* 0.016 0.018 0.064 0.143 BMI \* 0.004 0.011 0.075 0.319 Mageb \* 0.135 0.085 0.0003 0.009 reg \* 0.159 0.054 0.081 0.291 Chage \* 0.016 0.018 0.064 0.143

Table 4. Estimates of factor loadings of the LVM3 with only two indicators in Niegria.

Figure 1 shows the non-linear effect of the child's age to be associated with a malnutrition status in Nigeria for LVM1 and LVM2, respectively. It shows that the rates of malnutrition of children increase sharply from about 5 to around 20 months of age. The rates of malnutrition are at low level between 20 and 30 months of age, then rise again through the

are compared (LVM3) with analysis when all three indicators (LVM2) are present.

stunting λ11 \* 1.147 0.028 1.097 1.203 underweight λ21 \* 0.987 0.0274 0.934 1.040

 urban 0.0357 0.060 -0.357 0.152 anvis \* 0.346 0.075 0.205 0.492 toilet 0.156 0.082 -0.013 0.313 elect \* 0.153 0.058 0.033 0.269

 male <sup>11</sup> ( ) *a* \* 0.242 0.059 -0.357 -0.1372 work <sup>12</sup> ( ) *a* 0.087 0.064 -0.028 0.211 trepr <sup>13</sup> ( ) *a* 0.124 0.083 -0.044 0.290 water <sup>14</sup> ( ) *a* 0.065 0.086 -0.1033 0.241 educ <sup>15</sup> ( ) *a* \* 0.184 0.067 0.055 0.330 radio <sup>16</sup> ( ) *a* 0.019 0.0365 -0.049 0.088 male <sup>21</sup> ( ) *a* -0.057 0.045 -0.150 0.026 work <sup>22</sup> ( ) *a* \* 0.118 0.053 0.0155 0.224 trepr <sup>23</sup> ( ) *a* 0.022 0.060 -0.090 0.137 water <sup>24</sup> ( ) *a* 0.0079 0.069 -0.124 0.139 educ 25 ( ) *a* 0.046 0.0529 -0.051 0.154 radio <sup>26</sup> ( ) *a* 0.028 0.029 -0.027 0.089

seen to be more serious in Nigeria (its higher factor loading of 1.14).

remainder of the third year. This pattern highlights the first two years of life as the most nutritionally vulnerable for children in Nigeria.

Fig. 1. Nonlinear effects from top to bottom: child's age, mother's BMI and mother's age at birth for LVM1 (left) and LVM2 (right) of "malnutrition status" of children for Nigeria, using latent varaible model for continuous responses

The nonlinear effect of the BMI of the mother shows that obesity of the mother probably poses less of a risk for the child's nutritional status, due to the fact that a very low BMI suggested acute undernutrition of the mother. The Z-score is highest (and thus stunting lowest) at a BMI of around 30-40 months.

Associations Between Nutritional Indicators Using Geoadditive

"Malnutrion status" for Nigeria

Fig. 5. Map of Nigeria showing the different states

Latent Variable Models with Application to Child Malnutrition in Nigeria 555

Fig. 4. Posterior mean for Latent varaible model, using only two idicators of latent varaible

Fig. 2. Posterior mean for leatent varaiable model for LVM1 (left panel) and LVM2 (right panel) on malnutrion status for Nigeria

Fig. 3. Nonlinear effects from top to bottom: child's age, mother's BMI and mother's age at birth using only two indicators of latent varaible "malnutrition status" of children for Nigeria, using latent varaible model for continuous responses.

The effect of the mother's age seems to be slight on the Z-scores of children up till about the age of 25 months; thereafter, there is a strong effect shown.

Fig. 2. Posterior mean for leatent varaiable model for LVM1 (left panel) and LVM2 (right

Fig. 3. Nonlinear effects from top to bottom: child's age, mother's BMI and mother's age at birth using only two indicators of latent varaible "malnutrition status" of children for

The effect of the mother's age seems to be slight on the Z-scores of children up till about the

Nigeria, using latent varaible model for continuous responses.

age of 25 months; thereafter, there is a strong effect shown.

panel) on malnutrion status for Nigeria

Fig. 4. Posterior mean for Latent varaible model, using only two idicators of latent varaible "Malnutrion status" for Nigeria

Fig. 5. Map of Nigeria showing the different states

Associations Between Nutritional Indicators Using Geoadditive

**4.7 Availability of electricity and radio in household** 

negatively.

**4.5 Drinking water** 

availability of water.

**4.6 Access to toilet** 

with LVM) is better.

**4.8 Antenatal visits** 

positive effect.

**4.9 Child's age** 

Latent Variable Models with Application to Child Malnutrition in Nigeria 557

studies reported that when mothers are working, the household income is increased and the access to better food will be increased, as well as the access to a quality level of medical care. On the other hand, when mothers are employed outside the home, the duration of full breastfeeding is shortened and necessitates supplementary feeding. This is usually preformed by illiterate care-takers, which might affect the health of children

A household's source of drinking water has been shown to be associated with the nutritional status of a child in Nigeria (*weight-for-age*) in separate analysis (Khatab, 2007), and it seems to be mostly significant in the results of LVM. In other words, the source of water is associated with the nutritional status of a child through its impact on the risk of childhood diseases such as diarrhea, and is affected indirectly as a measure of wealth and

The type of toilet used by a household is an indicator of household wealth and a determinant of environmental sanitation. This means that poor households, which are mostly located in rural areas, are less likely to have sanitary toilet facilities. Consequently, this results in an increased risk of childhood diseases, which contributes to malnutrition. The results indicate that in households where a flush toilet exits, stunting and underweight (separate analysis) are significantly lower and the nutritional status of children (analysis

Despite access to electricity and radio, which facilitates the acquisition of nutritional information allowing more successful allocation of resources to produce child health (Kandala, 2001), only the availability of electricity was significant and had a positive effect on reducing stunting, and underweight with separate analysis, and it seems to be significant on the LVM "nutritional status". This may be because mothers allocate their leisure time to radio or television, but it doesn't help improve the level of nutrition of their children. At the same time,

The variables that deal with access to health care, such as children of mothers who obtained clinical visits during pregnancy and had vaccines and treatment, have a positive and significant effect on malnutrition status. Therefore, health service investments are more effective in reducing stunting, wasting and underweight among indigenous communities. Our results indicate that children of mothers who had clinical visits and got medical care during pregnancy are less likely to be stunted and to be underweight than their counterparts in Nigeria. The results with two indicators also indicate that the *anvis* has a

In the analysis, it was discovered that the situation among children who are stunted is quite similar; however, the deterioration in nutritional status is set between 5-20 months of age.

it reduces the length of time spent engaging in their children's affairs.(Kandala 2001)

In addition, the patterns of the nonlinear effect in LVM3 (Figure 3) are similar to the patterns of LVM1 and LVM2. The same is true with regard to the spatial effects of LVM3 (Figure 4). Figure 2 shows that the districts in the southeastern through the southern part of the country are associated with better nutrition of children in Nigeria.
