# Table 2 Definitions of variables and parameters

Type Symbol Definition/description Units
Random variables, observed values Λ, λ Per host net egg output eggs gram-1
W, w Per host mean weight of female Ascaris grams
n Per host female worm burden worms host-1
a Host age group (a = 0 for age ≤ 12, a = 1 for age > 12,)
Unobserved random variables M Per host unobserved true mean weight of female Ascaris grams
Unobserved values μ W Expected value of the per host mean weight of female Ascaris grams
μ Λ Expected value of the per host net egg output eggs gram-1
p The probability of observing a zero count from the Bernoulli process -
Estimated parameters $α a = { α 1 a , α 2 a , α 3 a } MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaeqySde2aaSbaaSqaaiabdggaHbqabaGccqGH9aqpcqGG7bWEcqaHXoqydaWgaaWcbaGaeGymaeJaemyyaegabeaakiabcYcaSiabeg7aHnaaBaaaleaacqaIYaGmcqWGHbqyaeqaaOGaeiilaWIaeqySde2aaSbaaSqaaiabiodaZiabdggaHbqabaGccqGG9bqFaaa@40F1@$ Describe the form of density-dependence of the expected value
of the per host mean weight of female Ascaris in age group a
-
$σ = { σ 1 2 , σ 2 2 } MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaaccmGae83WdmNaeyypa0Jaei4EaSNaeq4Wdm3aa0baaSqaaiabigdaXaqaaiabikdaYaaakiabcYcaSiabeo8aZnaaDaaaleaacqaIYaGmaeaacqaIYaGmaaGccqGG9bqFaaa@3A40@$ Describe the relationship between the variance of the per host
mean weight of female Ascaris and the female worm burden
-
λ 1 Exponential of the intercept term of statistical models fitting
the expected value of the per host net egg output to data
-
β Describes the effect of host age category on the expected
value of the per host net egg output
-
c An inverse measure of the severity of density dependence (0 <c ≤ 1)
on the expected value of the per host net egg output
-
$γ = { γ 1 , γ 2 , γ 3 } MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaeq4SdCMaeyypa0Jaei4EaSNaeq4SdC2aaSbaaSqaaiabigdaXaqabaGccqGGSaalcqaHZoWzdaWgaaWcbaGaeGOmaidabeaakiabcYcaSiabeo7aNnaaBaaaleaacqaIZaWmaeqaaOGaeiyFa0haaa@3BAF@$ Describe the form of the relationship between the expected value
of the per host net egg output and female Ascaris mean weight
-
$δ = { δ 0 , δ 1 , δ 2 , δ 3 } MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaeqiTdqMaeyypa0Jaei4EaSNaeqiTdq2aaSbaaSqaaiabicdaWaqabaGccqGGSaalcqaH0oazdaWgaaWcbaGaeGymaedabeaakiabcYcaSiabes7aKnaaBaaaleaacqaIYaGmaeqaaOGaeiilaWIaeqiTdq2aaSbaaSqaaiabiodaZaqabaGccqGG9bqFaaa@3F50@$ Describe the age-dependent relationship between the logit of the probability
of observing a zero egg count, the natural logarithm of female worm burden and
the natural logarithm of the mean weight of female Ascaris
-
k Inverse measure of the degree of overdispersion in egg output data -