The phrase "as a random coefficient" is correct and usable in written English.
It can be used in statistical or mathematical contexts, particularly when discussing models that include random coefficients to account for variability in data.
Example: "In our analysis, we treated the intercept as a random coefficient to better capture the differences across subjects."
Alternatives: "as a stochastic parameter" or "as a variable coefficient".
Therefore, using only nests with complete hatching success, I nested observation (N = 206) within offspring (N = 107) and offspring within brood (N = 49), each as a random coefficient on age and on the square of age.
The random coefficients were tested statistically to determine whether each should be retained as a random coefficient or could be included as fixed.
We matched controls on the birth cohort and accounted for year of birth as a random coefficient in a generalized linear mixed model that is recommended with this design (28, 29 ).
Thus it may not have been possible to detect significant variation in the effect of orphan status across the countries in our small sample when this was modeled as a random coefficient at the country level.
Analyses were conditional to the matching variable and based on univariate and multivariate generalized linear mixed models with the logit link function for the outcome and C0 as a random coefficient (28, 29 ).
To explore the possible association between pleural pressure change and several tested variables, we used the SAS MIXED procedure, building a mixed-effect linear model, in which each patient was treated as a random coefficient.
In a separate analysis of the patients as a group, a random coefficient cubic regression model was fitted to all the patient data using "proc MIXED".
Risk adjustment was achieved using a random coefficient (intercept as ICU site and slope as APACHE III score) logistic regression model, generating an expected mortality series.
Not surprisingly, as the underlying mortality estimates from a random coefficient model are obligatorily "smoothed" (see also Figure 1), no ARCH effects, representing "volatility", were demonstrated and a relatively simple seasonal autoregressive model was established (Table 1).
Risk adjustment was undertaken, generating the "expected" series, using a random coefficient logistic model (intercept as ICU site and "slope" as (centred) APACHE III score; unstructured covariance using adaptive quadrature, estimated via the Stata™ module "xtmelogit" [ 24]), as previously described in detail [ 20], and extended to both ventilated and non-ventilated patients.
A random coefficient model with all three parameters treated as local random parameters for each plot was fitted using the SAS macro NLINMIX (Littell et al., 1996).
