curvefit.core.effects2params

Map Vector of Fixed and Random Effects to Parameter Matrix

Extracts fixed and random effects and converts them to parameters. Needs to use unzip_x.

Syntax

params = curvefit.core.effects2params.effects2params(
    x, group_sizes, covs, link_fun, var_link_fun, expand=True
)

Arguments

• x (np.array): This is a one dimensional numpy array contain a value for the fixed effects followed by the random effects. The random effects are divided into sub-vectors with length equal to the number of fixed effects. The i-th sub-vector corresponds to the i-th group of observations.
• group_sizes (array-like): A vector of positive integers. The first group_sizes[0] observations correspond to the first group, the next group_sizes[1] corresponds to the section group, and so on. The total number of observations is the sum of the group sizes.
• covs (List[np.ndarray]): Is a list with length equal to the number of parameters and covs[k] is a two dimensional numpy array with the following contents: -- covs[k].shape[0] is the number of observations -- covs[k].shape[1] is the number of fixed effects corresponding to the k-th parameter. -- covs[k][i, ell] is the covariate value corresponding to the i-th observation and ell-th covariate for the k-th parameter.
• link_fun (List[Callable]): The valuelen(link_fun)is equal to the number of parameters andlink_fun[k]` is a function with one numpy array argument and result that acts element by element and transforms the k-th parameter.
• var_link_fun (List[Callable]): The valuelen(var_link_fun)is equal to the number of fixed effects andlink_fun[j]is a function with one numpy array argument and result that that acts element by element and transforms the j-th fixed effect. The firstlen(covs[0])fixed effects correspond to the first parameter, the nextlen(covs[1])` fixed effects correspond to the second parameter and so on.
• expand (bool): If expand is True (False), create parameters for each observation (for each group of observations).

Returns

• params (array-like): Let $f_j$ be the vector of fixed effects and $r_{i,j}$ the matrix of random effects corresponding to x. We define the matrix, with row dimension equal the number of groups and column dimension equal the number of fixed effects $$v_{i,j} = V_j \left( f_j + r_{i,j} \right)$$ where $V_j$ is the function var_link_fun[i]. If expand is true (false) $i$ indexes observations (groups). (If expand is true the random effect for a group gets repeated for all the observations in the group.) The return value params is a two dimensional numpy array with params.shape[0] equal to the number of parameters and params.shape[1] equal to the number of observations, if expand is true, number of groups, if expand is false. The value params[k][i] is $$P_k \left( \sum_{j(k)} v_j c_{i,j} \right)$$ where $P_k$ is the function link_fun[k], $j(k)$ is the set of fixed effects indices corresponding to the k-th parameter, $c_{i,j}$ is the covariate value corresponding to the j-th fixed effect and the i-th observation, if expand is true, or i-th group, if expand is false.

Example

See effects2params_xam.