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Fig 1.

Simulated data.

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Fig 2.

Simulated response vs. estimated response.

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Table 1.

Summary of the MSE for different values of m, ni, σ2, and for data simulated from a RIM in a logarithmic scale.

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Table 2.

Summary of the MSE for different values of m, ni, α, and for data simulated from a GLMM with gamma distribution and logarithmic link.

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Table 3.

Parameter estimations for the RIM associated with income in a logarithmic scale for elderly people data in 2016.

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Table 3 Expand

Fig 3.

Residuals.

Left: Histogram of the residuals. Middle: qq-plot of the residuals. Right: qq-plot of the residuals of the random effects.

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Fig 3 Expand

Fig 4.

Fitted values for the RIM associated with income in a logarithmic scale for elderly people data in 2016.

Squared red: naive estimates. Blue triangles: estimates by using the correction terms in (12).

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Table 4.

Summary of the MSE for the mimic simulation example.

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