Table 3.

Estimates of parameters in θ_free, under four different sets of constraints, for the small mammal index example. In ℳ₁ β₀₂ reached the lower bound used in the L-BFGS-B algorithm, which resembles the behaviour observed in study 1 associated with degenerate solutions. In ℳ₂ the fitted HSC is clearly not degenerate and corresponds to approximately 24% of the observations y. The AIC is reduced when more than one mode is allowed as in ℳ₃ although there is little evidence of the need for relaxing the equality constraint on α as in ℳ₄.

model	AIC	l	p	β 0	β 1	α	m
ℳ 1	3565.3	−1776.7	{0.30,0.70}	{−1.33,−15.00}	8.94	56.11	0.41
ℳ 2	3563.7	−1775.8	{0.76,0.24}	−2.52	{0.00,13.32}	76.45	0.38
ℳ 3	3556.7	−1771.4	{0.36,0.64}	−2.68	{3.72,3.87}	80.1	{0.30,0.53}
ℳ 4	3558.6	−1771.3	{0.35,0.65}	−2.68	{3.76,3.85}	{80.10,80.11}	{0.30,0.53}