LOTUS_regression.regression.mzm_regression(X, Y, sigma=None, tolerance=0.01, max_iter=50, do_autocorrelation=True, do_heteroscedasticity=False, extra_heteroscedasticity=None, heteroscedasticity_merged_flag=None, seasonal_harmonics=(3, 4, 6, 12), constrain_ilt_gap=False, ilt_predictor_index_dict=None)[source]

Performs the regression for a single bin.

  • X (np.ndarray) – (nsamples, npredictors) Array of predictor basis functions

  • Y (np.array) – (nsamples) Observations

  • sigma (np.array) – (nsamples) Square root of the diagonal elements of the covariance matrix for Y

  • tolerance (float, optional) – Iterations stop when the relative difference in the AR1 coefficient is less than this threshold. Default 1e-2

  • max_iter (int, optional) – Maximum number of iterations to perform. Default 50

  • do_autocorrelation (bool, optional) – If true, do the AR1 autocorrelation correction on the covariance matrix. Default True.

  • do_heteroscedasticity (bool, optional) – If True, do the heteroscedasticity correction on the covariance matrix. Default False.

  • extra_heteroscedasticity (np.ndarray, optional) – (nsamples, nextrapredictors) Extra predictor functions to use in the heteroscedasticity correction.

  • heteroscedasticity_merged_flag (np.ndarray, optional) – (nsamples) A flag indicating time periods that should be treated independently in the heteroscedasticity correction. E.g. this could be something like [0, 0, 0, 0, 2, 2, 2, 1, 1, 1] which would create 3 independant time periods where the heteroscedasticity correction is applied.

  • seasonal_harmonics (Iterable Float, optional. Default (3, 4, 6, 12)) – The monthly harmonics to use in the heteroscedasticity correction.

  • constrain_ilt_gap (bool, optional. Default False.) – If true then a constraint is added so that the ILT terms in the gap period enforce continuity. This must be set in conjunction with ilt_predictor_index_dict

  • ilt_predictor_index_dict (dict, optional. Default None.) – If using constrain_ilt_gap, this must be a dictionary {predictor_name: index_in X} which contains the indicies of the predictors ‘gap_cons’, ‘pre_const’, ‘post_const’, ‘gap_linear’, ‘linear_pre’, ‘linear_post’


results – a dictionary of outputs with keys: gls_results

The raw regression output. This is an instance of RegressionResults which is documented at


Residuals of the fit in the original coordinate system.


Residuals of the fit in the GLS transformed coordinates.


The AR1 correlation constant.


Number of iterative steps performed.


Calculated covariance of Y that is input to the GLS model.

Return type


LOTUS_regression.regression.regress_all_bins(predictors, mzm_data, time_field='time', debug=False, sigma=None, post_fit_trend_start=None, include_monthly_fits=False, return_raw_results=False, constrain_ilt_gap=False, **kwargs)[source]

Performs the regression for a dataset in all bins.

  • predictors (pd.Dataframe) – Dataframe of predictors to use in the regression. Index should be a time field.

  • mzm_data (xr.DataArray) – DataArray containing the monthly zonal mean data in a variety of bins. The data should be three dimensional with one dimension representing time. The other two dimensions are typically latitude and a vertical coordinate.

  • time_field (string) – Name of the time field in the mzm_data structure

  • sigma (xr.DataArray, optional. Default None) – If not None then the regression is weighted as if sigma is the standard deviation of mzm_data. Should be in the same format as mzm_data.

  • post_fit_trend_start (datetimelike, optional. Default None) – If set to a datetime like object (example: ‘2000-01-01’) then a linear trend is post fit to the residuals with the specified start date. If this is set you should not include a linear term in the predictors or the results will not be valid

  • constrain_ilt_gap (bool, optional. Default False) – If True then a constraint is added to the regression so that the fit terms in the gap period maintain continunity when doing ILT trends. The predictors must have keys ‘gap_cons’, ‘post_const’, ‘pre_const’, ‘linear_pre’, ‘linear_post’, and ‘gap_linear’ for this option to work. This is the standard case when using the ‘predictors_baseline_ilt_linear_gap’ file.

  • kwargs – Other arguments passed to mzm_regression


Return type