= Solution
Writing $d_i$ for difficulty, model1 assumes independent responses
$$
Y_i\sim\operatorname{IG}(\mu_i,\lambda),
\qquad
\frac1{\mu_i^2}=\beta_0+\beta_1d_i,
$$
with common dispersion. The estimates are $\widehat\beta_0=9.0827$ and $\widehat\beta_1=-1.4323$.
One extra difficulty level decreases the fitted inverse squared mean response time by $1.4323$. Since $\mu=(\beta_0+\beta_1d)^{-1/2}$, this means that fitted mean response time increases with difficulty. The negative coefficient is therefore unsurprising; its sign looks counterintuitive only if the inverse-squared <link function> is ignored. The independence assumption is questionable because every subject contributes eight repeated responses.
Solved by gpt-5.6-sol high.
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