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Four unsuccessful attempts have conditional probability ${\prod }_{j=1}^4{q}_j(y)$. The outcome is then unobserved, so the observed-data likelihood integrates over it:This is a probability, whereas a responder contributes a joint density in the observed outcome. The sequential response selection model keeps outcome-dependent nonresponse in the likelihood; evaluating the product at an imputed mean would not be this likelihood.

Write ${\mu }_i=\alpha +\beta z_i+{\gamma }^{\mathsf{T}}{x}_i$ and let $f_i(y)={\sigma }^{-1}\varphi ((y-{\mu }_i)/\sigma )$ be the normal distribution density. Set $q_j(y)=\mathrm{expit}({\eta }_j+\theta y)$, where $q_j$ is the probability that attempt $j$ is unsuccessful conditional on the preceding attempts being unsuccessful. This is a sequential response selection model. For first-attempt success, the observed outcome and attempt count contributeThis likelihood conditions on baseline and assignment; the displayed response probabilities do not use $d_i$. No factor for random allocation is needed when conditioning on its realized value.

Within the displayed sequential response selection model, $\theta =0$ makes every attempt's nonresponse probability independent of $Y$, and hence gives the outcome-independence needed for complete-case analysis. The estimate $\hat{\theta }=0.38$ suggests that larger outcomes are associated with greater odds of an unsuccessful attempt. Per one-unit outcome increase, the fitted odds ratio is $e^{0.38}\approx 1.46$, with the reported interval transformed to $(e^{-0.06},e^{0.82})\approx (0.94,2.27)$.

The confidence interval for $\theta$ includes zero, so there is no rejection of outcome-independent missingness at the five-percent level within this model. This does not establish that the missing at random assumption is true: the interval also allows appreciable outcome dependence, and inference depends on the chosen selection model. The intercepts describe response levels, not independence from the outcome. Nor can the respondents' mean and standard deviation establish the missing outcomes' distribution. There are $300-211=89$ unobserved outcomes, about $29.7\%$, so conclusions about the full trial depend materially on the missingness assumptions.