Ordinary least squares and linear mixed-effects: minimal examples

OLS and mixed-effect models are specified by model formulas. The results returned by statstmodels for OLS and lme4::lmer for mixed-effcts models populate the FitGrid object. The FitGrid[times, channels] can be sliced by times or channels with pandas index slicing. The results are accessed via the fit object attributes and returned as a pandas.DataFrame or another FitGrid[times, channels].

Generate simulated data and load Epochs

import fitgrid

epochs_df = fitgrid.generate(
    n_samples=6, n_channels=4, return_type="dataframe"
)
epochs_df.set_index(["epoch_id", "time"], inplace=True)
epochs_fg = fitgrid.epochs_from_dataframe(
    epochs_df,
    epoch_id="epoch_id",
    time="time",
    channels=["channel0", "channel1"],
)

Ordinary least squares (OLS)

These models are specified with patsy Python formulas like lm in R. The results come back via statsmodels as FitGrid[times, channels] objects populated with linear_model.RegressionResults.

lm_grid = fitgrid.lm(epochs_fg, RHS='1 + categorical + continuous', quiet=True)

Query and display OLS parameters

lm_grid.params

		channel0	channel1
time
0	Intercept	20.650048	5.585524
	categorical[T.cat1]	-35.120682	6.599356
	continuous	-14.775001	-9.338461
1	Intercept	0.683811	-12.571311
	categorical[T.cat1]	-5.206154	-21.539669
	continuous	-35.775448	45.342606
2	Intercept	-12.530338	11.251361
	categorical[T.cat1]	14.008110	-13.685990
	continuous	10.068809	12.267045
3	Intercept	12.766953	21.057617
	categorical[T.cat1]	-18.569296	8.686739
	continuous	3.264109	-51.767878
4	Intercept	-6.559106	-5.279575
	categorical[T.cat1]	12.145254	3.802076
	continuous	-25.433041	36.160998
5	Intercept	17.456711	-14.128496
	categorical[T.cat1]	6.525926	0.118656
	continuous	-41.083032	26.952374

Query and display parameter standard errors

lm_grid.bse

		channel0	channel1
time
0	Intercept	12.552213	12.402446
	categorical[T.cat1]	12.901155	12.747224
	continuous	22.928736	22.655161
1	Intercept	13.916252	15.612712
	categorical[T.cat1]	15.399735	17.277039
	continuous	30.691683	34.433151
2	Intercept	13.398024	15.459433
	categorical[T.cat1]	16.387789	18.909201
	continuous	27.346612	31.554138
3	Intercept	14.410638	13.244376
	categorical[T.cat1]	13.168739	12.102985
	continuous	21.257582	19.537192
4	Intercept	13.998653	15.979570
	categorical[T.cat1]	12.407299	14.163028
	continuous	24.230742	27.659579
5	Intercept	17.236837	18.165900
	categorical[T.cat1]	14.679198	15.470405
	continuous	25.211903	26.570821

params = lm_grid.params
params.index = params.index.set_names(["time", "params"])
for param, vals in params.groupby("params"):
    ax = vals.reset_index("params", drop=True).plot()
    ax.set_title(param)

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Linear mixed effects (LMER)

These models are specified with lme4::lmer R formulas and the results come back via pymer4 as FitGrid[times, channels] objects populated with Lmer objects from the lme4::lmer and lmerTest results.

Fit a mixed-effects model with lme4::lmer via pymer4

lmer_grid = fitgrid.lmer(
    epochs_fg, RHS='1 + continuous + (continuous | categorical)', quiet=True
)

Out:

boundary (singular) fit: see ?isSingular

boundary (singular) fit: see ?isSingular

boundary (singular) fit: see ?isSingular

boundary (singular) fit: see ?isSingular

boundary (singular) fit: see ?isSingular

boundary (singular) fit: see ?isSingular

boundary (singular) fit: see ?isSingular

boundary (singular) fit: see ?isSingular

boundary (singular) fit: see ?isSingular

boundary (singular) fit: see ?isSingular

Query and display some lme4::lmer fit results

lmer_grid.coefs

			channel0	channel1
time
0	(Intercept)	Estimate	3.50231	9.06438
		2.5_ci	-24.8492	-10.9472
		97.5_ci	31.8539	29.0759
		SE	14.4653	10.2102
		DF	1.32568	18
...	...	...	...	...
5	continuous	SE	24.4753	36.2556
		DF	18	0.867252
		T-stat	-1.62512	0.578611
		P-val	0.121517	0.677492
		Sig

96 rows × 2 columns