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"cell_type": "markdown",
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"source": [
"# National mathematics example\n",
"Here we provide a usage example of the IRTorch package using data from the national mathematics test for Swedish high school students. We will not do an in-depth analysis of the data, but rather showcase some of the main features of IRTorch to enable the user to analyze their own data.\n",
"\n",
"Users are referred to the API reference section of the documentation for more detailed information of different functions and classes. Note that the results might vary slightly from those presented here due to differences in the computing hardware (CPU or GPU), the operating system, and the versions of the packages used.\n",
"\n",
"If you prefer to run the code directly, you can download this example Jupyter notebook from the [GitHub repository](https://github.com/joakimwallmark/irtorch/blob/main/docs/source/notebooks/national_mathematics.ipynb)."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Load the libraries\n",
"We start by loading the libraries and modules that we will use for this example."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import pandas as pd\n",
"import numpy as np\n",
"import torch\n",
"import irtorch\n",
"from irtorch.models import GeneralizedPartialCredit, MonotoneNN\n",
"from irtorch.rescale import Bit\n",
"from irtorch.estimation_algorithms import MML, JML"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
""
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
" \n",
" "
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import plotly\n",
"plotly.offline.init_notebook_mode()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## The test data\n",
"The package requires the data to be in a PyTorch tensor with test takers as rows and items as columns. The item responses should be coded 0, 1, ... and missing responses coded as `nan`. If you have, for example, a pandas dataframe, you can convert it to a tensor using `torch.tensor(df.to_numpy())`. This is illustrated with some random data below."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"tensor([[3., nan, 1., 2., 3.],\n",
" [nan, nan, nan, 3., 0.],\n",
" [2., 4., 3., 3., 3.],\n",
" [4., 1., 0., 0., nan],\n",
" [nan, 3., 0., 2., 1.],\n",
" [1., 1., nan, nan, 0.],\n",
" [2., 3., 2., 2., 1.],\n",
" [2., 4., 1., 4., 4.],\n",
" [2., 0., 3., nan, nan],\n",
" [4., 3., 3., 1., 3.]], dtype=torch.float64)\n"
]
}
],
"source": [
"np.random.seed(42)\n",
"example_df = pd.DataFrame({f\"Item {i}\": np.random.randint(0, 5, 10) for i in range(1, 6)})\n",
"missing_indices = np.random.choice(example_df.index, size=10, replace=False)\n",
"for col in example_df.columns:\n",
" example_df.loc[np.random.choice(missing_indices, size=2, replace=False), col] = np.nan\n",
"\n",
"example_tensor = torch.tensor(example_df.to_numpy())\n",
"print(example_tensor)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In this example, we will use data from the Swedish national mathematics test. Two datasets from this test are provided within the package and we will use the second one. Feel free to explore the first one one you own, using `irtorch.load_dataset.swedish_national_mathematics_1()`."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"data_math = irtorch.load_dataset.swedish_national_mathematics_2()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Construct the model\n",
"We start by creating a Generalized Partial Credit (GPC) model. It requires the number of possible responses/scores for each item but these can be automatically computed from the data when supplied."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"irtorch.set_seed(42)\n",
"gpc = GeneralizedPartialCredit(data=data_math)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In the same fashion, we initialize a more flexible Monotone Neural Network (MNN) model for comparison. For more details on these IRT models and other available models, see the [IRT Models](./../irt_models.rst) section."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"irtorch.set_seed(42)\n",
"mnn = MonotoneNN(data = data_math)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Fitting the model"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Each model can now be fit using the `fit()` instance method. `fit()` requires the model training data as a tensor, together with an instance of the chosen fitting algorithm. In these examples, we will use the MML algorithm for the GPC model and the JML algorithm for the MNN model.\n",
"\n",
"We recommend splitting your test data into a training and a test set to ensure we are not overfitting the model as below. Fitting will be done using the GPU if available, otherwise the CPU will be used. This can also be specified using the `device` argument, i.e., `gpc.fit(train_data=data_math, algorithm=AE(), device = \"cpu\")`. Currently available fitting algorithms can be found in the [Estimation algorithms](./../estimation_algorithms.rst) section with additional information on how to fine tune each algorithm."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Epoch: 193. Loss: 20799.9922 "
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"INFO: Stopping training after 2 learning rate updates.\n",
"INFO: Best model found at iteration 193 with loss 20799.9922.\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Epoch: 2017. Loss: 18708.7871 "
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"INFO: Decreased learning rate to: 0.05\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Epoch: 2523. Loss: 18691.8711 "
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"INFO: Decreased learning rate to: 0.025\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Epoch: 2607. Loss: 18690.8984 "
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"INFO: Best model found at iteration 2607 with loss 18690.8984.\n"
]
}
],
"source": [
"irtorch.set_seed(42)\n",
"train_data, test_data = irtorch.split_data(data_math, 0.8)\n",
"gpc.fit(train_data=train_data, algorithm=MML())\n",
"mnn.fit(train_data=train_data, algorithm=JML())"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The `plot` property of our models contains methods for visualization. We can plot the training history to check if we appear to have converged to a good solution. We see that the loss function appear to have converged for both models. In our experience, there is usually slight improvements from training for more iterations even when the loss appears relatively flat. This is especially true for more flexible models. Refer to the [Plotting](./../plotter.rst) section for more information on the available plotting methods."
]
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"theta_train_mnn = mnn.latent_scores(train_data, theta_estimation=\"ML\")\n",
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"The latent scales are arbitrary and can thus be transformed to any other scale as long as the transformation maintains the ordering of the scores. This can be done by providing a scale transformation object to the `add_scale_transformation` model method. For these models, we suggest converting the latent trait scales to *bit scales* instead. Bit scales are ratio scales, and make scores from different models comparable as long as they are fitted to the same test data. We create `Bit` class instances and supply them to the `add_scale_transformation` method for each model. \n",
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"INFO: Converged at iteration 4.\n",
"INFO: Finding training data theta scores to use as initial theta estimates...\n",
"INFO: Sampling training data theta scores to avoid running out of memory...\n",
"INFO: Optimizing theta scores...\n"
]
},
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"INFO: Converged at iteration 6.\n"
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"gpc_bit_transformation = Bit(gpc, population_theta=theta_train_gpc)\n",
"mnn_bit_transformation = Bit(mnn, population_theta=theta_train_mnn)\n",
"gpc.add_scale_transformation(gpc_bit_transformation)\n",
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"bit_scores_train_gpc = gpc.latent_scores(train_data, theta_estimation=\"ML\")\n",
"bit_scores_train_mnn = mnn.latent_scores(train_data, theta_estimation=\"ML\")"
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"If we plot the bit score distribution for each model, we can see that they are more similar compared to the distributions of the original latent variables, both scales ranging from 0 to around 80 bits."
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"## Item response functions\n",
"To show the item response functions, we can use the `item_probabilities()` method in the `plot` model property. Here we plot the curves for item 24 on the bit scale. We can see that the probability of answering the item correctly increases with the latent variable. We see that only test takers with a relatively high bit score have a high probability of responding with a score of 2 on this item."
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"## Item parameters\n",
"For parametric IRT models such as the GPC model, we can get the estimated item parameters using the `item_parameters()` method. We use the `irt_format` argument to specify that we want to return the item parameters in traditional IRT format (and not as slopes and intercepts). Note that zeros are expected for items with fewer than 4 points."
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