Ethnic Differences in Child Overweight/Obesity Prevalence and Trajectories

Two Worlds of Obesity:

Ethnic Differences in Child Overweight/Obesity Prevalence and Trajectories.

Methodological Appendix

This appendix provides statistical details not included in the text. Table A-1 compares the characteristics of students in schools that were excluded from the analysis (n=84) with the students in the analysis sample (n=6333). The only significant difference was in ethnicity. All of the excluded schools were small rural schools and had, in total, only 4 Hispanic students.

Table A-2 parallels Table 2 in the text but focuses on the categorical measure of obesity and overweight rather than the BMI-Z scores, reporting the percentage of students in each ethnic group who were overweight and obese by grade, year and sex.

Table A-3 gives the correlation matrix of all variables used in the analysis. The top section of the table gives the results for the cross-sectional sample and the remaining two sections give the results for the two panel samples.

Tables A-4, 5, and 6 provide details on the mixed model analyses of the cross-sectional data. Tables A-4 gives the model fit statistics of all models tested in the mixed model analysis with the full cross-sectional sample. The top panel of Table A-4 summarizes the models that were tested. Model 1 was the base-line, intercept only model. Model 2 added ethnicity; Model 3 added the dummy variables associated with grade, year and sex; and Model 4 added the school level measure of receipt of free or reduced lunch. Models 5 to 8 separately added each set of interaction effects separately; and Model 9 included all of the possible two-way interactions with ethnicity. The fit statistics and random effects parameters associated with each model with the BMI-Z scores as the dependent measure are in the second panel. The -2*Log Likelihood statistics has a chi-square distribution and changes in the statistics from one model to the next can be examined to see if a given model provides a significantly better fit. Each of the models with the interaction terms (Models 5 to 9) provides a significantly better fit than the model with only the main effect (Model 4), indicating that Model 9, with all of the two-way interaction effects is the most appropriate one to consider. The third panel of the table gives the model fit statistics when a categorical measure of overweight and obesity (with normal weight as the 0 category) was used. Table A-5 parallels Table 3 in the text and gives the coefficients associated with Models 4 and 9 in Table A-4. Table A-6 reports the model fit statistics for the tests of additional interaction effects for the analyses within ethnic groups.

Table A-7 gives descriptive data for the two panel samples. Table A-8 compares the characteristics of the panel samples with the total group. Only one of the 14 comparisons (not one of the measures of overweight or obesity) was statistically significant, a result that would be expected by chance.

TableA-9 reports the fit statistics for the mixed model analyses for the panel samples, and Table A-10 gives the coefficients associated with the categorical analysis.

Table A-1
Inferential Tests Comparing Characteristics of Students in Schools Excluded from the Analysis with Students in the Included Schools
Variable / Inferential Test and Results
Categorical Measure of Weight / Chi-square = 3.14, df = 2, p = .21
BMI-Z Scores / t = 1.66, df = 6414 p = .10
Ethnicity / Chi-square = 9.92, df = 1, p = .002
Male / Ch-square = 1.04, df = 1, p = .31
FRL % in School / t = 0.61, df = 6, 414, df = .54
82 students were in the four schools omitted from the analysis
Table A-2
Distribution in Weight Categories of Hispanic and Non-Hispanic White Students, by Grade, Year, and Sex, Cross-Sectional Sample
Hispanic Students / Non-Hisp.White Students
% Overweight / % Obese / % Overweight / % Obese
Total Group / 18.8 / 33.4 / 18.6 / 18.0
By Grade
Grade 1 / 19.5 / 26.0 / 18.5 / 15.8
Grade 3 / 18.2 / 34.6 / 17.7 / 17.3
Grade 5 / 18.8 / 40.0 / 19.7 / 21.1
By Year
2005 / 15.8 / 27.3 / 18.2 / 18.3
2006 / 17.0 / 37.3 / 20.7 / 18.7
2007 / 19.9 / 28.1 / 17.4 / 16.3
2008 / 20.1 / 37.2 / 18.4 / 18.6
By Sex:
Female / 19.9 / 29.4 / 19.5 / 17.1
Male / 17.7 / 37.5 / 17.8 / 18.9
The percentage of students in the normal weight category can be calculated by subtracting the sum of the overweight and obese groups from 100. Sample sizes are in Table 2 in the text.
Table A-3
Correlation Matrices, Cross-Sectional and Panel Samples
Cross-Sectional Sample (n=6333)
BMI-Z / Hispanic / Male / Grade / Year / FRL
BMI-Z / 1.00
Hispanic / 0.15 / 1.00
Male / 0.03 / -0.02 / 1.00
Grade / 0.04 / -0.01 / 0.01 / 1.00
Year / 0.01 / 0.07 / 0.01 / 0.00 / 1.00
FRL / 0.08 / 0.22 / -0.01 / -0.01 / 0.06 / 1.00
Panel Sample, Grade 1 to Grade 3 (n = 276)
BMI-Z, Gr. 3 / BMI-Z, Gr 1 / Hispanic / Male / FRL
BMI-Z, Gr. 3 / 1.00
BMI-Z, Gr 1 / 0.82 / 1.00
Hispanic / 0.30 / 0.23 / 1.00
Male / 0.07 / 0.02 / -0.05 / 1.00
FRL / 0.19 / 0.08 / 0.42 / 0.00 / 1.00
Panel Sample, Grade 3 to Grade 5 (n = 212)
BMI-Z, Gr. 5 / BMI-Z, Gr 3 / Hispanic / Male / FRL
BMI-Z, Gr. 5 / 1.00
BMI-Z, Gr 3 / 0.83 / 1.00
Hispanic / 0.26 / 0.15 / 1.00
Male / 0.02 / 0.00 / 0.06 / 1.00
FRL / 0.03 / -0.01 / 0.21 / 0.07 / 1.00
Table A-4
Models and Fit Statistics for Mixed Model Regression of BMI-Z Scores on Ethnicity, Grade, Year, Sex, and Poverty Level of School, Cross-Sectional Sample
Elements of the Models
Models / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9
Hispanic / X / X / X / X / X / X / X / X
Grade / X / X / X / X / X / X / X
Year / X / X / X / X / X / X / X
Sex / X / X / X / X / X / X / X
FRL-School / X / X / X / X / X / X
FRL*Hispanic / X / X
Grade*Hispanic / X / X
Year*Hispanic / X / X
Sex*Hispanic / X / X
Fit Statistics - BMI-Z Dependent
1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9
Fit Statistics
Log Likelihood / -8897 / -8836 / -8811 / -8811 / -8808 / -8807 / -8806 / -8809 / -8798
- 2 LL / 17794 / 17672 / 17623 / 17622 / 17617 / 17614 / 17612 / 17619 / 17596
Dif / 121.7 / 49.4 / 1.1 / 4.9 / 7.4 / 9.8 / 3.2 / 25.7
df change / 1 / 6 / 1 / 1 / 2 / 3 / 1 / 8
Prob. / <.001 / <.001 / <.30 / <.05 / <.05 / <.05 / <.10 / <.01
Random Effects
SD Constant / 0.12 / 0.10 / 0.12 / 0.11 / 0.11 / 0.11 / 0.11 / 0.11 / 0.11
SD Residual / 0.98 / 0.97 / 0.97 / 0.97 / 0.97 / 0.97 / 0.97 / 0.97 / 0.97
Fit - Statistics - Categorical Variable Dependent
Log Likelihood / -4236 / -4195 / -4174 / -4173 / -4171 / -4170 / -4169 / -4171 / -4163
- 2 LL / 8471 / 8390 / 8347 / 8345 / 8342 / 8341 / 8337 / 8342 / 8326
Dif / 80.8 / 43.2 / 1.8 / 3.5 / 4.3 / 7.8 / 3.4 / 19.6
df change / 1 / 6 / 1 / 1 / 2 / 3 / 1 / 8
Prob. / <.001 / <.001 / <.20 / <.10 / <.10 / <.02 / <.10 / <.02
Note: Models 5, 6, 7, 8 and 9 are all compared with Model 4.
Table A-5
Mixed Model Logistic Regressions of Categorical Measure of Overweight and Obesity on Ethnicity, Time, Grade, Sex, FRL, Main Effects Only and with Interactions with Ethnicity, Cross-Sectional Sample
Only Main Effects / Including Interactions with Ethnicity
b / Z / b / Z
Hispanic / 0.60 / 8.87*** / 0.95 / 2.68**
Year 2006 / 0.13 / 1.36 / 0.47 / 2.18*
Year 2007 / -0.13 / -1.41 / 0.17 / 0.84
Year 2008 / 0.07 / 0.94 / 0.58 / 3.07**
Grade 3 / 0.12 / 1.86 / 0.06 / 0.87
Grade 5 / 0.34 / 5.18*** / 0.28 / 3.84***
Male / 0.05 / 0.99 / 0.26 / 2.21*
FRL (School Level) / 0.00 / 1.41 / 0.00 / 1.83
Hispanic * Year 2006 / ----- / ----- / -0.38 / -1.68
Hispanic * Year 2007 / ----- / ----- / -0.33 / -1.5
Hispanic * Year 2008 / ----- / ----- / -0.60 / -2.95**
Hispanic * Grade 3 / ----- / ----- / -0.25 / -1.55
Hispanic * Grade 5 / ----- / ----- / -0.28 / -1.71
Hispanic * Male / ----- / ----- / -0.26 / -1.94*
Hispanic * FRL / ----- / ----- / -0.01 / -1.93*
Constant / -0.97 / -5.60*** / -0.93 / -5.21***
Note: There were 18 schools in the analysis. The number of students per school ranged from 26 to 706 with an average of 352 students per school. The dependent measure is a dummy variable with 1 = overweight or obese and 0 = normal weight.
***, p < .001; **, p < .01; *, p<.05
Table A-6
Models and Fit Statistics for Mixed Model Regression of BMI-Z Scores on Ethnicity, Grade, Year, Sex, and Poverty Level of School, Cross-Sectional Sample
Elements of the Models
Models / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9
Grade / X / X / X / X / X / X / X / X
Year / X / X / X / X / X / X / X / X
Sex / X / X / X / X / X / X / X / X
FRL-School / X / X / X / X / X / X / X
Grade * Year / X
Grade * Male / X
Grade * FRL / X
Year * Male / X
Year * FRL / X
Male *FRL / X
Fit Statistics and Random Effects, Hispanics
1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9
Fit Statistics
Log Likelihood / -1652 / -1634 / -1634 / -1631 / -1634 / -1633 / -1634 / -1630 / -1633
- 2 LL / 3305 / 3269 / 3268 / 3262 / 3267 / 3266 / 3268 / 3261 / 3267
Dif / 36.16 / 0.62 / 6.22 / 0.82 / 2.04 / 0.28 / 7.54 / 1.44
df change / 3 / 1 / 6 / 2 / 2 / 3 / 3 / 1
Prob. / <.001 / ns / ns / ns / ns / ns / <.10 / ns
Random Effects
SD Constant / 0.11 / 0.11 / 0.11 / 0.11 / 0.11 / 0.10 / 0.11 / 0.98 / 0.11
SD Residual / 1.00 / 0.98 / 0.98 / 0.04 / 0.98 / 0.98 / 0.98 / 0.97 / 0.98
Fit Statistics and Random Effects, Non-Hispanic Whites
1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9
Log Likelihood / -7182 / -7167 / -7166 / -7164 / -7165 / -7164 / -7165 / -7164 / -7165
- 2 LL / 14365 / 14333 / 14331 / 14329 / 14330 / 14329 / 14329 / 14328 / 14331
Dif / 31.44 / 1.90 / 2.54 / 1.84 / 2.78 / 2.32 / 3.1 / 0.6
df change / 3 / 1 / 6 / 2 / 2 / 3 / 3 / 1
Prob. / <.001 / <.20 / ns / ns / ns / ns / ns / ns
Random Effects
SD Constant / 0.12 / 0.10 / 0.12 / 0.11 / 0.11 / 0.11 / 0.11 / 0.11 / 0.11
SD Residual / 0.98 / 0.97 / 0.97 / 0.97 / 0.97 / 0.97 / 0.97 / 0.97 / 0.97
Models four through nine are all compared to Model 3
Table A-7
Average BMI-Z and Percentage Overweight and Obese of Hispanic and Non-Hispanic White Students, by Grade, Panel Samples
Panel 1: Grade 1 to Grade 3
Average BMI-Z / % Overweight or Obese
Hispanic / Non-Hispanic White / Hispanic / Non-Hispanic White
Grade 1 / 1.27 / 0.66 / 56% / 36%
Grade 3 / 1.42 / 0.58 / 67% / 35%
Panel 2: Grade 3 to Grade 5
Average BMI-Z / % Overweight or Obese
Hispanic / Non-Hispanic White / Hispanic / Non-Hispanic White
Grade 3 / 1.08 / 0.73 / 53 / 38
Grade 5 / 1.30 / 0.68 / 63 / 38
Table A-8
Comparison of Panel Sample to Total Cross-Sectional Sample on Key Characteristics
Means / Z-Scores Comparisons
Cross-Sectional / Panel Grades 1 to 3 / Panel Grades 3 to 5 / Panel 1-3 to X Sect. / Panel 3-5 to X-Sect.
BMI-Z / 0.74 / 0.76 / 0.80 / 0.35 / 0.96
BMI-Z / 0.74 / 0.72 / 0.80 / -0.33 / 0.95
% Overweight or Obese / 0.39 / 0.39 / 0.42 / -0.12 / 0.60
% Overweight or Obese / 0.39 / 0.40 / 0.43 / 0.12 / 1.16
% Hispanic / 0.18 / 0.16 / 0.20 / -0.89 / 0.72
% Male / 0.52 / 0.50 / 0.52 / -0.66 / 0.08
% FRL / 55.75 / 48.87 / 54.52 / -6.50 / -1.02
Note: The first entry for the measures of weight status in the columns with panel data is for the baseline year and the second entry is for the second year. Z-scores were calculated using the standard formula for comparing a sub-sample (the panel group) to the population (the cross-sectional sample), dividing the difference of the two averages by the standard error. The standard error is calculated as the standard deviation of the population divided by the square root of the sample size. Only one of the 14 z-scores was statistically significant, a result that would be expected by chance.
Table A-9
Models and Fit Statistics, Panel Samples
Characteristics of Models Examined
1 / 2 / 3 / 4 / 5 / 6
BMI-Z Baseline / X / X / X / X / X
Hispanic / X / X / X / X
Male / X / X / X / X
FRL (school) / X / X / X / X
Hispanic * Baseline / X
Hispanic * Male / X
Hispanic * FRL / X
Fit Statistics, BMI-Z Dependent Measure, Grade 1-3 Panel
Log Likelihood / -401 / -247 / -241 / -241 / -241 / -240.19
- 2 Log Likelihood / 802 / 494 / 482 / 482 / 482 / 480.38
Dif / 308.0 / 12.0 / 0.00 / 0.00 / 1.62
df change / 1 / 3 / 1 / 1 / 1
Prob. / <.001 / <.01 / ns / ns / <.30
Random Effects
SD Constant / 0.24 / 0.20 / 0.10 / 0.11 / 0.10 / 0.11
SD Residual / 1.02 / 0.58 / 0.57 / 0.57 / 0.57 / 0.57
Fit Statistics, BMI-Z Dependent Measure, Grade 3-5 Panel
Log Likelihood / -292 / -164 / -156 / -155 / -156 / -154.09
- 2 Log Likelihood / 584 / 328 / 312 / 310 / 312 / 308.18
Dif / 256.0 / 16.0 / 2.0 / 0.000 / 3.82
df change / 1 / 3 / 1 / 1 / 1
Prob. / <.001 / <.01 / <.20 / ns / <.10
Random Effects
SD Constant / .09*10(-9) / 0.16 / 0.16 / 0.18 / 0.16 / 0.16
SD Residual / 0.96 / 0.51 / 0.49 / 0.49 / 0.49 / 0.49
Fit Statistics, Categorical Dependent Measure, Grade 1-3 Panel
Log Likelihood / -185.59 / -123.15 / -117.67 / -115.15 / -117.67 / -117.52
- 2 Log Likelihood / 371.18 / 246.3 / 235.34 / 230.3 / 235.34 / 235.04
Dif / 124.9 / 11.0 / 5.04 / 0.00 / 0.30
df change / 1 / 3 / 1 / 1 / 1
Prob. / <.001 / <.02 / <.05 / n.s. / n.s.
Fit Statistics, Categorical Dependent Measure, Grade 3-5 Panel
Log Likelihood / -145.09 / -96.51 / -93.75 / -93.07 / -93.7 / -93.05
- 2 Log Likelihood / 290.18 / 193.02 / 187.5 / 186.14 / 187.4 / 186.1
Dif / 97.2 / 5.5 / 1.4 / 0.100 / 1.4
df change / 1 / 3 / 1 / 1 / 1
Prob. / <.001 / <.20 / <.30 / n.s. / <.30
Table A-10
Mixed Model Logistic Regressions of Categorical Measure of Overweight and Obesity, Panel Samples
Grade 1 to 3 Panel
b / Z
Overweight/Obese Gr. 1 / 3.21 / 8.89***
Male / 0.25 / 0.74
Hispanic / 1.20 / 2.43**
FRL (School Level) / 0.01 / 1.04
Baseline (Gr. 1) * Hispanic / ----- / -----
Constant / -2.64 / -4.59***
Grade 3 to 5 Panel
b / Z
Overweight/Obese Gr. 1 / 3.17 / 8.37***
Male / -0.23 / -0.61
Hispanic / 1.01 / 2.12
FRL (School Level) / 0.002 / 0.27
Constant / -1.89 / -3.18***
***, p < .001; **, p < .01; *, p<.05

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