“…Dependent variables and the residuals of the initially tested linear regression models were not normally distributed; therefore, inverse Gaussian regression models were used to estimate the random effect of the s th calf and the fixed effects of deltamethrin treatment, the sampling occasion, and the farm on the SC and CK levels, flies' number, and daily consumption of concentrates and roughages, as described below: Y jkns = µ + T j + S k + F n + γ s + e jkns (Model 1) where Y jkns = dependent variable (SC and CK levels, number of flies landed on a calf within a 2-min period, and daily consumption of concentrates and roughages), µ = intercept, T j = fixed effect of calves group (j = 2 levels, 0 = Deltamethrin treated group, 1 = Control group), S k = fixed effect of the sampling occasion (k = 5 levels, Days 15,25,35,45, and 55, for daily consumption of concentrates and roughages k = 4 levels, Days 25, 35, 45 and 55), F n = fixed effect of the farm (n = 2 levels, 0 = farm A, 1 = farm B), γ s = repeated variation of the s th calf, and e jkns = residual error. In every case, first order autoregressive was used as covariance structure.…”