A Framework of Statistical Tests For Comparing Mean and Covariance Structure Models

Temporal patterning in blood glucose (BG) consistent with fractals—how BG follows a repetitive pattern through resolutions of time—was used to examine 2 different samples of adolescents with Type 1 diabetes (10–14 years). Sample 1 contained 10 adolescents with longtime series for accurate estimations of long-term dependencies associated with fractals. The second contained 94 adolescents measured multiple times daily over a 2-week period corresponding to psychosocial measures. In both samples, temporal dependencies in BG showed patterns consistent with fractals. In the second sample, temporal dependencies were associated with indicators of vigilant regulation including adolescents' higher anxiety, mothers' higher monitoring, and intrusive support. The existence of temporal dependencies in BG moderated the relationship between glycosylated hemoglobin (Hb_A1c) and indicators of low BG risk but not the relationship between Hb_A1c and high BG risk. These results show how a biomedical indicator may be susceptible to metric issues associated with fractals.