A data set from the 1994 General Social Survey on subjects’ opinions on four items (the environment, health, law enforcement, education) related to whether they believed government spending on each item should increase, stay the same, or decrease. Subjects were also classified by their gender and race. For subject i, let G_i = 1 for females and 0 for males, let R_1i = 1 for whites and 0 otherwise, R_2i = 1 for blacks and 0 otherwise, and R_1i = R_2i = 0 for the other category of race. Let Y_it denote the response for subject i on spending item t, where outcomes (1, 2, 3) represent (increase, stay the same, decrease).

With constraint β₄ = 0, the random-intercept model

logit[P(Y_it ≤ j|u_i)] = α_j + β_t + β_g G_i + β_r1 R_i1 + β_r2 R_2i + u_i, j = 1, 2,

has β̂₁ = –0.55, β̂₂ = –0.60, β̂₃ = –0.49, with σ̂ = 1.03. These estimates are greater than five standard errors in absolute value. Interpret.