Use dedicated simultaneous-treatment dataset for MultiPeriodDiD tutorial

Instead of explaining rank deficiency behavior, create a clean dataset
using generate_did_data() with simultaneous treatment timing. This shows
MultiPeriodDiD working as intended without warnings or edge cases.

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

Author: igerber

docs/tutorials/02_staggered_did.ipynb

@@ -671,7 +671,7 @@
   {
    "cell_type": "markdown",
    "metadata": {},
-   "source": "## 11. Comparing with MultiPeriodDiD\n\nFor comparison, here's how you would use `MultiPeriodDiD` which estimates period-specific effects. \n\n**Important**: `MultiPeriodDiD` assumes **simultaneous treatment timing** (all treated units get treated at the same time). For staggered adoption, always use `CallawaySantAnna` or `SunAbraham` instead.\n\nTo demonstrate `MultiPeriodDiD` properly, we'll filter to a single treatment cohort (cohort 3) plus never-treated units.\n\n**Note on rank deficiency**: `MultiPeriodDiD` creates a design matrix with period dummies and treatment interactions. Depending on the data structure, this can create linear dependencies. When this happens, the solver will:\n- Emit a warning listing the dropped columns\n- Set coefficients of dropped columns to NA\n- Compute valid estimates for the remaining (identified) parameters\n\nThis R-style handling ensures you get useful results while being warned about the structural issue."
+   "source": "## 11. Comparing with MultiPeriodDiD\n\nFor comparison, here's how you would use `MultiPeriodDiD` which estimates period-specific effects. \n\n**Important**: `MultiPeriodDiD` assumes **simultaneous treatment timing** (all treated units get treated at the same time). For staggered adoption, always use `CallawaySantAnna` or `SunAbraham` instead.\n\nTo demonstrate `MultiPeriodDiD` properly, we'll create a simple dataset where all treated units receive treatment at the same time."
   },
   {
    "cell_type": "code",
@@ -685,7 +685,7 @@
     }
    },
    "outputs": [],
-   "source": "# Filter to cohort 3 only (single treatment timing) plus never-treated\n# This is the appropriate data structure for MultiPeriodDiD\ncohort3_df = df[df['cohort'].isin([0, 3])].copy()\n\nmp_did = MultiPeriodDiD()\nresults_mp = mp_did.fit(\n    cohort3_df,\n    outcome=\"outcome\",\n    treatment=\"treated\",\n    time=\"period\",\n    post_periods=[3, 4, 5, 6, 7]\n)\n\nprint(results_mp.summary())"
+   "source": "# Create a simple dataset with simultaneous treatment timing\n# This is the appropriate data structure for MultiPeriodDiD\nfrom diff_diff import generate_did_data\n\n# Generate data with simultaneous treatment at period 4\nmp_data = generate_did_data(\n    n_units=100,\n    n_periods=8,\n    treatment_period=4,  # All treated units get treatment at period 4\n    treatment_fraction=0.5,\n    treatment_effect=2.5,\n    seed=42\n)\n\nprint(f\"MultiPeriodDiD dataset: {len(mp_data)} obs\")\nprint(f\"Treatment starts at period 4 for all treated units\")\n\nmp_did = MultiPeriodDiD()\nresults_mp = mp_did.fit(\n    mp_data,\n    outcome=\"outcome\",\n    treatment=\"treated\",\n    time=\"period\",\n    post_periods=[4, 5, 6, 7]\n)\n\nprint(results_mp.summary())"
   },
   {
    "cell_type": "code",