"ValueError: `times` coords already set" when `n_media_times = n_times + max_lag`

Hi!

I am trying to incorporate media "burn-in" effects by having `n_media_times = n_times + max_lag`, as described in the [API reference](https://developers.google.com/meridian/reference/api/meridian/data/input_data/InputData) (media attribute). I suspect that there is an issue in the code though as the [DataFrameInputDataBuilder.with_media](https://developers.google.com/meridian/reference/api/meridian/data/data_frame_input_data_builder/DataFrameInputDataBuilder#with_media) method sets `time_col`. In contrast, the [DataFrameInputDataBuilder.with_organic_media](https://developers.google.com/meridian/reference/api/meridian/data/data_frame_input_data_builder/DataFrameInputDataBuilder#with_organic_media) sets `media_time_col`.

Thus when I have my input dataframe that has `max_lag` more rows in the beginning for my media data than for my kpi I get the following error:

---------------------------------------------------------------------------

ValueError                                Traceback (most recent call last)

Cell In[107], line 13

      1 data_loader = DataFrameDataLoader(

      2     df=df,

      3     coord_to_columns=coord_to_columns,

   (...)

     11     #organic_frequency_to_channel=organic_frequency_to_channel,

     12 )

---> 13 data = data_loader.load()


File /opt/conda/lib/python3.10/site-packages/meridian/data/load.py:759, in DataFrameDataLoader.load(self)

    754   # So now we can use one of the channel mapper dicts to get the canonical

    755   # channel names for each column.

    756   media_channel_names = [

    757       self.media_to_channel[c] for c in self.coord_to_columns.media

    758   ]

--> 759   builder.with_media(

    760       self.df,

    761       media_execution_columns,

    762       media_spend_columns,

    763       media_channel_names,

    764       self.coord_to_columns.time,

    765       self.coord_to_columns.geo,

    766   )

    768 if (

    769     self.reach_to_channel is not None

    770     and self.frequency_to_channel is not None

   (...)

    774   # listed in `reach`, `frequency`, and `rf_spend` are already validated

    775   # to correspond to the same channels, in user-given order.

    776   reach_columns = list(self.coord_to_columns.reach)

File /opt/conda/lib/python3.10/site-packages/meridian/data/data_frame_input_data_builder.py:381, in DataFrameInputDataBuilder.with_media(self, df, media_cols, media_spend_cols, media_channels, time_col, geo_col)

    379 media_spend_data = media_df.set_index([geo_col, time_col])[media_spend_cols]

    380 media_spend_data.columns = media_channels

--> 381 self.media_spend = (

    382     media_spend_data.stack()

    383     .rename(constants.MEDIA_SPEND)

    384     .rename_axis([

    385         constants.GEO,

    386         constants.TIME,

    387         constants.MEDIA_CHANNEL,

    388     ])

    389     .to_xarray()

    390 )

    391 return self

File /opt/conda/lib/python3.10/site-packages/meridian/data/input_data_builder.py:338, in InputDataBuilder.media_spend(self, media_spend)

    336 self._media_spend = self._normalize_coords(media_spend, constants.TIME)

    337 self.geos = self.media_spend.coords[constants.GEO].values.tolist()

--> 338 self.time_coords = self.media_spend.coords[constants.TIME].values.tolist()

File /opt/conda/lib/python3.10/site-packages/meridian/data/input_data_builder.py:85, in InputDataBuilder.time_coords(self, value)

     83   raise ValueError('`times` coords must be unique.')

     84 if self.time_coords is not None and set(self.time_coords) != set(value):

---> 85   raise ValueError(f'`times` coords already set to {self.time_coords}.')

     86 if self.media_time_coords is not None and not set(value).issubset(

     87     self.media_time_coords

     88 ):

     89   raise ValueError(

     90       '`times` coords must be subset of previously set `media_times`'

     91       ' coords.'

     92   )

ValueError: `times` coords already set to ['2022-07-21', '2022-07-22', ...

It seems that there is a mismatch in the time value, which stems from the fact that my media data has more rows than my remaining data.

Start at DataFrameDataLoader.load in meridian/data/load.py, then inspect with_media in meridian/data/data_frame_input_data_builder.py and the time_coords setter in meridian/data/input_data_builder.py. Compare the media and KPI time-coordinate handling with with_organic_media. Done means media data can include the documented additional burn-in times without triggering the existing coordinate mismatch error.

Written by the indexing model from the issue text.