Based on n × p data matrix X, whose rows r i (j = 1,…, n) tally to observational variables and whose columns c j (j = 1,…, p) are the individuals of the corresponding variables, the ICA model of X can be written as (4) X = A S. With generality intact, A is a n × n mixing matrix, whereas S is a n × p source matrix under the necessity of S being statistically independent as possible.
This paper uses data collected by five burn centers, two in the UK, one in Belgium and two in the USA, to develop and validate a probabilistic model of burn healing time, as a function of the laser-Doppler flux measurements, and of demographic and observational variables.
Related questions addressed were what was the best blood flow summary statistic and whether, given the blood flow measurements, demographic and observational variables had any additional predictive power (age, sex, race, % total body surface area burned (%TBSA), site and cause of burn, day of LDI scan, burn center).
Before considering the laser-Doppler measurements as predictors of healing time, it is worthwhile modeling healing time purely as a function of demographic and observational variables.
This is, whether, given laser-Doppler blood flow measurements, demographic and observational variables have any further predictive ability, or whether the blood flow measurement recorded as mean flux in PU is a sufficient statistic (see [ 9] for a definition of this term).
The following 2 nonrandomized observational variables represented compliance: the total number of tablets consumed and duration of supplementation.
The means, standard deviations, and bivariate correlations for all the observational variables are shown in Table 3.
Although this will have been a small fraction of our total sample size and unlikely to have materially altered our main results, it may have led to underestimates of both observational and instrumental variable estimates.
In previous applications we assumed that all models θ have the same causal structure, i.e. considering multivariate random variables a t and o t, we assumed that the same variables a t are intervened for all θ and the same causal model is used to predict the consequences of these interventions on the observational variables o t.
To assess construct validity, a compliance task was utilized to determine whether children identified as high on anxiety/withdrawal, anger/aggression, or social competence with the parent version of the SCBE-30 (n=20 for each group) could be distinguished behaviorally on several observational variables.
