### Load Holzinger39 Example Data

Source: https://gitlab.com/georgy.m/semopy/-/blob/master/notebooks/semopy - Walkthrough.ipynb

Retrieves the model description and dataset from the built-in Holzinger39 example to demonstrate handling stratified data.

```python
from semopy.examples import holzinger39
desc, data = holzinger39.get_model(), holzinger39.get_data()
print(desc)
data.head()
```

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

### Import semopy and Example Models

Source: https://gitlab.com/georgy.m/semopy/-/blob/master/notebooks/model_modelmeans.ipynb

Imports the necessary Model and ModelMeans classes from the semopy library, along with various example model definitions. These examples serve as a basis for demonstrating model fitting functionalities.

```python
from semopy import Model, ModelMeans
from semopy.examples import *

models_info = (
univariate_regression,
               univariate_regression_many,
               multivariate_regression,
               holzinger39,
               political_democracy,
               example_article,
               # example_rf
               )

```

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

### Configure Model Parameters with New Syntax

Source: https://context7.com/georgy.m/semopy/llms.txt

This snippet demonstrates the updated syntax for defining starting values and parameter bounds directly within the model specification string.

```python
new_syntax_model = """
f =~ x1 + x2 + x3

# Set starting value
start(0.5) _b1

# Set parameter bounds
bound(0.1 0.9) _b1
"""
```

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

### Install Semopy using Pip

Source: https://gitlab.com/georgy.m/semopy/-/blob/master/README.md

This command installs the semopy package from PyPi. It ensures all necessary dependencies are downloaded and configured for use in your Python environment.

```bash
pip install semopy
```

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

### Parameter Estimation Methods in Python with Model.fit()

Source: https://context7.com/georgy.m/semopy/llms.txt

Illustrates the use of the `fit()` method in semopy's `Model` class to estimate parameters using different objective functions and optimization algorithms. It shows examples for MLW, ULS, GLS, and FIML, including handling missing data with FIML and using custom solvers.

```python
from semopy import Model
from semopy.examples import holzinger39
import pandas as pd

# Classic Holzinger-Swineford CFA model
desc = """
visual =~ x1 + x2 + x3
textual =~ x4 + x5 + x6
speed =~ x7 + x8 + x9
"""

data = holzinger39.get_data()
model = Model(desc)

# Fit with default Maximum Likelihood Wishart (MLW)
result_ml = model.fit(data, obj='MLW')
print(f"MLW - Converged: {result_ml.success}, Fun: {result_ml.fun:.6f}")

# Fit with Unweighted Least Squares
model2 = Model(desc)
result_uls = model2.fit(data, obj='ULS')
print(f"ULS - Converged: {result_uls.success}, Fun: {result_uls.fun:.6f}")

# Fit with Generalized Least Squares
model3 = Model(desc)
result_gls = model3.fit(data, obj='GLS')
print(f"GLS - Converged: {result_gls.success}, Fun: {result_gls.fun:.6f}")

# Fit with Full Information Maximum Likelihood (handles missing data)
# FIML requires complete data matrix, not just covariance matrix
model4 = Model(desc)
result_fiml = model4.fit(data, obj='FIML')
print(f"FIML - Converged: {result_fiml.success}, Fun: {result_fiml.fun:.6f}")

# Fit with custom solver and constraints
model5 = Model(desc)
result_custom = model5.fit(data, obj='MLW', solver='L-BFGS-B')
print(f"L-BFGS-B - Converged: {result_custom.success}")

```

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

### GET /model/visualize

Source: https://gitlab.com/georgy.m/semopy/-/blob/master/notebooks/semopy - Walkthrough.ipynb

Generates a visual graph representation of the SEM model using Graphviz.

```APIDOC
## GET /model/visualize

### Description
Creates a visual representation of the SEM model and saves it to a file.

### Method
GET

### Endpoint
/model/visualize

### Parameters
#### Query Parameters
- **filename** (string) - Required - The path to save the generated graph file (e.g., 'model.pdf').

### Request Example
{
  "filename": "t.pdf"
}

### Response
#### Success Response (200)
- **graph** (object) - The Graphviz Digraph object representing the model structure.
```

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

### Model Random Effects with Semopy

Source: https://gitlab.com/georgy.m/semopy/-/blob/master/notebooks/semopy - Walkthrough.ipynb

This example illustrates the construction of an artificial model with a known covariance matrix of residuals, often used for modeling random effects. It involves generating random parameters, factor scores, and then incorporating random effects to simulate their impact on the data. This is particularly useful in fields like GWAS.

```python
import pandas as pd
np.random.seed(1)
n = 100 # Number of data samples
p = 3 # Number of indicators per latent factor
# Generating random parameters
params = [np.random.uniform(0.2, 1.2, size=(p - 1, 1)),
          np.random.uniform(0.2, 1.2, size=(p -1, 1))]
params = list(map(lambda x: np.append([1], x), params))
y = np.random.normal(size=(n, 2 * p))
# Generating factor scores
eta1 = np.random.normal(scale=1, size=(n, 1))
eta2 = np.random.normal(scale=1, size=(n, 1)) + 3 * eta1
# Loading factors onto indicators
y[:, :p] += np.kron(params[0], eta1)
y[:, p:] += np.kron(params[1], eta2)

# Intercepts!
means = np.random.normal(scale=3, size=2 * p)
y += means
params.append(means)

# Finally, random effects are here. They mess the data and there is nothing we could do...
u = np.random.normal(scale=3, size=y.shape)
y += u
```

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

### Inspect SEMopy Model Matrices

Source: https://context7.com/georgy.m/semopy/llms.txt

Extracts matrix representations of model estimates or starting values. This is useful for debugging model structure and viewing regression coefficients, factor loadings, and covariances.

```python
matrices = model.inspect(mode='mx', what='est')
print(matrices['beta'])
print(matrices['lambda'])
print(matrices['psi'])
start_matrices = model.inspect(mode='mx', what='start')
print(start_matrices['lambda'])
```

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

### GET /model/stats

Source: https://gitlab.com/georgy.m/semopy/-/blob/master/notebooks/semopy - Walkthrough.ipynb

Calculates and retrieves fit indices for the evaluated SEM model.

```APIDOC
## GET /model/stats

### Description
Computes popular fit indices such as CFI, GFI, RMSEA, AIC, and BIC to evaluate model performance.

### Method
GET

### Endpoint
/model/stats

### Parameters
None

### Response
#### Success Response (200)
- **stats** (object) - A collection of statistical metrics including DoF, chi2, CFI, GFI, and RMSEA.

#### Response Example
{
  "CFI": 0.988,
  "RMSEA": 0.055,
  "AIC": 60.85
}
```

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

### Fitting SEM Models with Model and ModelEffects

Source: https://gitlab.com/georgy.m/semopy/-/blob/master/notebooks/semopy - Walkthrough.ipynb

Demonstrates how to initialize and fit structural equation models using the standard Model class and the ModelEffects class for LMM-style analysis. Both methods allow for inspecting the model results after fitting.

```python
from semopy import Model, ModelEffects

# Standard Model fitting
m = Model(desc)
m.fit(data, groups=['school'])
ins = m.inspect()

# ModelEffects fitting
me = ModelEffects(desc)
me.fit(data, group='school')
ins_effects = me.inspect()
```

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

### Initialize and Fit Semopy Model

Source: https://gitlab.com/georgy.m/semopy/-/blob/master/notebooks/model_modelmeans.ipynb

This snippet demonstrates how to load model data and descriptions, initialize the semopy Model class, and fit the model to the provided data.

```python
art_data, art_desc = example_article.get_data(), example_article.get_model()
print(art_desc)
art_model = Model(art_desc)
art_model.fit(art_data)
print(art_model.inspect())
```

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

### Define and Instantiate a SEM Model

Source: https://gitlab.com/georgy.m/semopy/-/blob/master/notebooks/semopy - Walkthrough.ipynb

Demonstrates how to retrieve a model description string and instantiate a Model object in semopy.

```python
from semopy.examples import multivariate_regression
from semopy import Model

desc = multivariate_regression.get_model()
m = Model(desc)
```

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

### Define and Fit Basic SEM Model in Python

Source: https://context7.com/georgy.m/semopy/llms.txt

Demonstrates how to define a basic structural equation model using semopy's intuitive syntax, load data, fit the model, and inspect the results. It covers measurement and structural models, as well as residual correlations.

```python
from semopy import Model
from semopy.examples import political_democracy
import pandas as pd

# Get example model and data
desc = """
# Measurement model: latent variables are defined by indicators
ind60 =~ x1 + x2 + x3
dem60 =~ y1 + y2 + y3 + y4
dem65 =~ y5 + y6 + y7 + y8

# Structural model: regressions between latent variables
dem60 ~ ind60
dem65 ~ ind60 + dem60

# Residual correlations
y1 ~~ y5
y2 ~~ y4 + y6
y3 ~~ y7
y4 ~~ y8
y6 ~~ y8
"""

# Load the Political Democracy dataset
data = political_democracy.get_data()

# Create and fit the model
model = Model(desc)
result = model.fit(data)

# Check if optimization converged
print(f"Optimization success: {result.success}")
print(f"Objective function value: {result.fun:.4f}")

# Inspect parameter estimates with standard errors and p-values
estimates = model.inspect()
print(estimates)

# Output includes columns: lval, op, rval, Estimate, Std. Err, z-value, p-value

```

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

### Fit and Inspect Model in Semopy

Source: https://gitlab.com/georgy.m/semopy/-/blob/master/notebooks/semopy - Walkthrough.ipynb

This code snippet shows how to instantiate a semopy Model with a given description, fit the model to the provided data, and then inspect the results. The inspection provides detailed statistics for each parameter in the model, including estimates, standard errors, z-values, and p-values.

```python
m = Model(desc)
m.fit(data)
ins = m.inspect()
ins
```

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

### Load Data and Estimate SEM Model Parameters in Python

Source: https://gitlab.com/georgy.m/semopy/-/blob/master/README.md

This Python code shows the process of loading a dataset using pandas and then estimating the parameters of an initialized semopy Model. The `fit` method takes the dataset as input and uses default or specified objective functions and optimization methods.

```python
from pandas import read_csv
data = read_csv("my_data_file.csv", index_col=0)
model.fit(data)
```

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

### Fit Model and Inspect Results

Source: https://gitlab.com/georgy.m/semopy/-/blob/master/notebooks/semopy - Walkthrough.ipynb

Shows how to fit a model to a dataset and use the inspect method to retrieve parameter estimates in a pandas DataFrame.

```python
from semopy.examples import multivariate_regression

data = multivariate_regression.get_data()
r = m.fit(data)
ins = m.inspect()
```

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

### Load and Inspect Political Democracy Model in Semopy

Source: https://gitlab.com/georgy.m/semopy/-/blob/master/notebooks/semopy - Walkthrough.ipynb

This snippet demonstrates how to load a predefined model for the Political Democracy dataset using semopy, print the model description, and display the first few rows of the data. It serves as an initial step for analyzing the model's structure and data.

```python
from semopy.examples import political_democracy
desc = political_democracy.get_model()
data = political_democracy.get_data()
print(desc)
data.head()
```

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

### Define and Fit a Structural Equation Model

Source: https://context7.com/georgy.m/semopy/llms.txt

This snippet demonstrates how to define a model using the semopy syntax, including measurement and structural components, and how to fit it to data using the Model class.

```python
from semopy import Model

full_model = """
# Measurement model
f =~ x1 + x2 + x3

# Structural model
y1 ~ f + z
y2 ~ f

# Residual covariances
y1 ~~ y2
x1 ~~ x2
"""

model = Model(full_model)
model.fit(data)
print(model.inspect())
```

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

### Regularize Specific Loadings in Semopy

Source: https://context7.com/georgy.m/semopy/llms.txt

Demonstrates how to apply specific regularization (e.g., smooth L1) to particular parameters within a structural equation model using semopy. This allows for targeted shrinkage of coefficients.

```python
reg_specific = create_regularization(
    model3,
    regularization='l1-smooth',
    c=0.1,
    alpha=1e-5,
    param_names={'_b1', '_b2'}
)

result3 = model3.fit(data, regularization=reg_specific)
print("\nSelectively regularized estimates:")
print(model3.inspect())
```

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

### Apply Regularization to SEM Models

Source: https://context7.com/georgy.m/semopy/llms.txt

Explains how to use create_regularization to apply L1 (LASSO) or L2 (Ridge) penalties to specific model matrices like Lambda or Beta. This is essential for variable selection and reducing model complexity.

```python
from semopy import Model, create_regularization
from semopy.examples import holzinger39

desc = holzinger39.get_model()
data = holzinger39.get_data()
model = Model(desc)
model.load(data)

reg_l1 = create_regularization(model, regularization='l1-thresh', c=0.1, mx_names={'lambda'})
result = model.fit(data, regularization=reg_l1)
print(model.inspect())
```

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

### Inspect Model Parameters in Python with Model.inspect()

Source: https://context7.com/georgy.m/semopy/llms.txt

Explains how to use the `inspect()` method of the semopy `Model` class to retrieve detailed parameter estimates. It covers obtaining basic estimates, standardized coefficients, and robust standard errors (Huber-White).

```python
from semopy import Model
from semopy.examples import holzinger39

desc = holzinger39.get_model()
data = holzinger39.get_data()

model = Model(desc)
model.fit(data)

# Get basic estimates
estimates = model.inspect()
print("Basic parameter estimates:")
print(estimates)

# Get estimates with standardized coefficients
estimates_std = model.inspect(std_est=True)
print("\nWith standardized estimates:")
print(estimates_std[['lval', 'op', 'rval', 'Estimate', 'Est. Std']])

# Get robust standard errors (Huber-White sandwich correction)
estimates_robust = model.inspect(se_robust=True)
print("\nWith robust standard errors:")
print(estimates_robust)

```

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

### Fit Latent Variable Models with ModelMeans

Source: https://context7.com/georgy.m/semopy/llms.txt

Demonstrates how to define a measurement and structural model using Semopy's ModelMeans class. It covers data generation, model fitting using ML and REML objectives, and predicting missing values.

```python
import numpy as np
import pandas as pd
from semopy import ModelMeans

np.random.seed(42)
n = 200
x1, x2 = np.random.normal(0, 1, n), np.random.normal(0, 1, n)
eta = 0.5 * x1 + 0.3 * x2 + np.random.normal(0, 0.5, n)
data = pd.DataFrame({'x1': x1, 'x2': x2, 'y1': 0.8 * eta + np.random.normal(0, 0.3, n), 'y2': 0.7 * eta + np.random.normal(0, 0.3, n), 'y3': 0.9 * eta + np.random.normal(0, 0.3, n)})

desc = """eta =~ y1 + y2 + y3
eta ~ x1 + x2"""

model = ModelMeans(desc, intercepts=True)
result = model.fit(data, obj='ML')
print(model.inspect())
```

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

### Fit Semopy Model with ULS Objective Function in Python

Source: https://gitlab.com/georgy.m/semopy/-/blob/master/notebooks/semopy - Walkthrough.ipynb

This code snippet demonstrates how to initialize a Semopy model, fit it to data using the 'ULS' (Unweighted Least Squares) objective function, and then inspect the results. It highlights the flexibility in choosing objective functions for model estimation.

```python
m = Model(desc)
print(m.fit(data, obj='ULS'))
m.inspect()
```

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

### Visualize SEM Model with Graphviz

Source: https://gitlab.com/georgy.m/semopy/-/blob/master/notebooks/semopy - Walkthrough.ipynb

Visualizes a fitted structural equation model (SEM) using the graphviz library, saving the output to a PDF file. The generated graph object can be further manipulated if the dot-language is known.

```python
from semopy import semplot
g = semplot(m, filename='t.pdf')
g
```

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

### Implement Random Effects SEM with ModelEffects

Source: https://context7.com/georgy.m/semopy/llms.txt

Shows how to handle clustered data using the ModelEffects class. This includes defining random effects, fitting models with ML/REML, and calculating Best Linear Unbiased Predictors (BLUPs).

```python
from semopy import ModelEffects
import pandas as pd
import numpy as np

# Setup clustered data
n_groups, n_per_group = 20, 15
groups = np.repeat(range(n_groups), n_per_group)
data = pd.DataFrame({'x': np.random.normal(0, 1, n_groups * n_per_group), 'group': groups})

desc = """y1 ~ x
y2 ~ x
y1 ~~ y2"""

model = ModelEffects(desc, effects={'group'})
result = model.fit(data, group='group', obj='ML')
blup = model.calc_blup()
```

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

### Apply Parameter Constraints and Bounds

Source: https://context7.com/georgy.m/semopy/llms.txt

This snippet shows how to apply advanced parameter constraints and bounds within the semopy model syntax to restrict parameter values during estimation.

```python
constrained_model = """
f =~ x1 + x2 + x3
y1 ~ f

# Advanced: bound parameters
BOUND(0, 1) _b1

# Advanced: custom constraints
CONSTRAINT(_b1 + _b2 < 1)
"""
```

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

### Visualize SEM Models with semplot

Source: https://context7.com/georgy.m/semopy/llms.txt

Generates graphical diagrams of SEM models using Graphviz. Supports customization of parameter estimates, standardized values, covariances, and layout engines.

```python
from semopy import semplot
semplot(model, 'model_estimates.png', plot_ests=True)
semplot(model, 'model_standardized.png', plot_ests=True, std_ests=True)
semplot(model, 'model_view.png', show=True)
```

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

### Visualize Semopy Model

Source: https://gitlab.com/georgy.m/semopy/-/blob/master/notebooks/model_modelmeans.ipynb

This snippet shows how to use the semplot utility to generate a visual representation of the fitted model and save it to a PDF file.

```python
from semopy import semplot
plot = semplot(art_model, "art_model.pdf")
```

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

### Generate HTML Analysis Reports

Source: https://context7.com/georgy.m/semopy/llms.txt

Creates a comprehensive HTML report containing model specifications, parameter estimates, fit indices, and path diagrams. Facilitates documentation and sharing of analysis results.

```python
from semopy import report
report(model, 'Political_Democracy_Analysis')
report(model, 'Political_Democracy_Standardized', std_est=True)
```

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

### Constructing Semopy Model Description and Data

Source: https://gitlab.com/georgy.m/semopy/-/blob/master/notebooks/semopy - Walkthrough.ipynb

Generates a model description string and prepares a pandas DataFrame for structural equation modeling. It dynamically creates latent variable relationships and formats the data for model fitting.

```python
k = u @ u.T
res = list()
d = {'eta1': list(), 'eta2': list()}
y_names = list()
for i in range(1, p + 1):
    res.append((f'y{i}', '~', 'eta1', params[0][i - 1]))
    res.append((f'y{i}', '~', '1', params[2][i - 1]))
    y_names.append(res[-1][0])
    d['eta1'].append(y_names[-1])
for j in range(1, p + 1):
    res.append((f'y{j + i}', '~', 'eta2', params[1][j - 1]))
    res.append((f'y{j + i}', '~', '1', params[2][i + j - 1]))
    y_names.append(res[-1][0])
    d['eta2'].append(y_names[-1])
desc = '\n'.join(f"{eta} =~ {' + '.join(ys)}" for eta, ys in d.items())
desc += '\neta2 ~ eta1'
params = pd.DataFrame.from_records(res, columns=['lval', 'op', 'rval', 'est'])
data = pd.DataFrame(np.append(np.append(y, eta1, axis=1), eta2, axis=1),
                    columns=y_names + ['eta1', 'eta2'])
data = data.drop(['eta1', 'eta2'], axis=1)
data['group'] = data.index
```

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

### Modify Model Syntax

Source: https://gitlab.com/georgy.m/semopy/-/blob/master/notebooks/semopy - Walkthrough.ipynb

Illustrates how to append new relationships to an existing model description string.

```python
desc += '\nx1 ~ x3'
m = Model(desc)
m.fit(data)
ins = m.inspect()
```

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

### Define and Initialize SEM Model in Python

Source: https://gitlab.com/georgy.m/semopy/-/blob/master/README.md

This Python code snippet demonstrates how to define a Structural Equation Model (SEM) using semopy's syntax and initialize a Model object. The model string specifies structural and measurement parts, including latent variables and their relationships.

```python
from semopy import Model
mod = """
          x1 ~ x2 + x3
          x3 ~ x2 + eta1
          eta1 =~ y1 + y2 + y3
          eta1 ~ x1
      """
model = Model(mod)
```

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

### Inspect SEM Model Parameter Estimates in Python

Source: https://gitlab.com/georgy.m/semopy/-/blob/master/README.md

After fitting a semopy model, this Python code snippet demonstrates how to inspect the estimated parameters. The `inspect()` method provides a detailed view of the model's coefficients, standard errors, and other relevant statistics.

```python
model.inspect()
```

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

### Efficient Prediction with Exogenous Variables

Source: https://gitlab.com/georgy.m/semopy/-/blob/master/notebooks/semopy - Walkthrough.ipynb

Utilizes the predict_exo method in ModelMeans or ModelEffects to perform fast predictions of output variables based on known exogenous variables.

```python
import semopy
from semopy import ModelMeans

desc = semopy.examples.univariate_regression.get_model()
data = semopy.examples.univariate_regression.get_data()
m = ModelMeans(desc)
m.fit(data_train)
preds = m.predict_exo(data_test.drop(['y'], axis=1))
```

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

### Semopy Model Syntax Reference

Source: https://context7.com/georgy.m/semopy/llms.txt

This section details the concise syntax used in semopy for defining structural equation models. It covers operators for measurement, regression, and covariance, as well as methods for fixing parameters and specifying equality constraints.

```python
from semopy import Model
import pandas as pd
import numpy as np

np.random.seed(42)
n = 300

eta = np.random.normal(0, 1, n)
x1, x2, x3 = 0.7*eta + np.random.normal(0, 0.5, (3, n))
y1 = 0.8*eta + np.random.normal(0, 0.5, n)
y2 = 0.6*eta + np.random.normal(0, 0.5, n)
z = np.random.normal(0, 1, n)

data = pd.DataFrame({
    'x1': x1, 'x2': x2, 'x3': x3,
    'y1': y1, 'y2': y2, 'z': z
})

measurement_model = """
f =~ x1 + x2 + x3
"""

regression_model = """
y1 ~ x1 + x2
"""

covariance_model = """
x1 ~~ x2
x1 ~~ x1
"""

fixed_model = """
f =~ 1*x1 + x2 + x3
y1 ~ 0.5*x1 + x2
"""

equality_model = """
f =~ a*x1 + a*x2 + x3
"""

full_model = """

```

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

### Fit and Inspect SEM Models with semopy

Source: https://gitlab.com/georgy.m/semopy/-/blob/master/notebooks/model_modelmeans.ipynb

Iterates through a list of SEM model definitions, extracts data and model descriptions, and fits each model using both `Model` and `ModelMeans` classes with the default 'MLW' objective function. The `inspect()` method is called to display the results of each fit, including parameter estimates, standard errors, z-values, and p-values.

```python
for info in models_info:
    data, desc = info.get_data(), info.get_model()
    print(f"{'-\
'*20}
{desc}
")
    for model_class in (Model, ModelMeans):
        m = model_class(desc)
        m.fit(data)  # obj: MLW
        print(m.inspect())

```

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

### Print SEM Model Graphviz Definition

Source: https://gitlab.com/georgy.m/semopy/-/blob/master/notebooks/semopy - Walkthrough.ipynb

Prints the definition of the SEM model in the dot-language format, which is used by Graphviz for visualization. This allows for manual editing and understanding of the model's structure.

```python
print(g)
```

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

### Define SEM Measurement Model and Regressions

Source: https://gitlab.com/georgy.m/semopy/-/blob/master/notebooks/model_modelmeans.ipynb

This snippet demonstrates how to define latent variables using the =~ operator and specify regression relationships using the ~ operator in Semopy.

```text
# measurement model
ind60 =~ x1 + x2 + x3
dem60 =~ y1 + y2 + y3 + y4
dem65 =~ y5 + y6 + y7 + y8
# regressions
dem60 ~ ind60
dem65 ~ ind60 + dem60
```

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

### Evaluating ModelMeans Performance

Source: https://gitlab.com/georgy.m/semopy/-/blob/master/notebooks/semopy - Walkthrough.ipynb

Fits a model using ModelMeans and calculates the mean relative error compared to true parameters. This serves as a baseline for comparison.

```python
m = ModelMeans(desc)
m.fit(data)
ins = m.inspect()
errs = list()
for _, row in params.iterrows():
    t = (ins['op'] == row['op']) & (ins['lval'] == row['lval']) &\
        (ins['rval'] == row['rval'])
    t = ins[t]
    est = t['Estimate'].values[0]
    errs.append(abs((est - row['est']) / row['est']))
err = np.mean(errs)
print("Mean relative error: {:.3f}%".format(err * 100))
```

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

### Predicting Latent Factor Scores

Source: https://gitlab.com/georgy.m/semopy/-/blob/master/notebooks/semopy - Walkthrough.ipynb

Shows how to extract latent factor scores from a fitted structural equation model using the predict_factors method.

```python
desc = political_democracy.get_model()
data = political_democracy.get_data()
m = Model(desc)
m.fit(data)
factors = m.predict_factors(data)
print(factors.head())
```

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

### Estimate Intercepts using ModelMeans

Source: https://gitlab.com/georgy.m/semopy/-/blob/master/notebooks/semopy - Walkthrough.ipynb

The recommended approach for estimating intercepts in semopy. It involves initializing the ModelMeans class, fitting the model to the data, and inspecting the results for statistical significance.

```python
from semopy import ModelMeans
m = ModelMeans(desc)
m.fit(data)
m.inspect()
```

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

### Generalized Prediction and Data Imputation

Source: https://gitlab.com/georgy.m/semopy/-/blob/master/notebooks/semopy - Walkthrough.ipynb

Demonstrates how to use the predict method to impute missing values in datasets using a fitted semopy model.

```python
import numpy as np
from semopy import Model

desc = political_democracy.get_model()
data = political_democracy.get_data()
m = Model(desc)
# Introduce missing values
data.values[mask_x, mask_y] = np.nan
# Model handles missing data by default
```

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

### Estimate Intercepts using estimate_means

Source: https://gitlab.com/georgy.m/semopy/-/blob/master/notebooks/semopy - Walkthrough.ipynb

Demonstrates the use of the estimate_means function on a fitted model to retrieve intercept values. Note that this method is generally considered less reliable for statistical inference.

```python
from semopy import estimate_means
means = estimate_means(m)
means
```

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

### POST /model/fit

Source: https://gitlab.com/georgy.m/semopy/-/blob/master/notebooks/semopy - Walkthrough.ipynb

Fits a structural equation model to the provided dataset and generates predictions.

```APIDOC
## POST /model/fit

### Description
Fits the SEM model using the FIML estimator and returns predictions based on the input data.

### Method
POST

### Endpoint
/model/fit

### Parameters
#### Request Body
- **data** (DataFrame) - Required - The input dataset used for model fitting and prediction.

### Request Example
{
  "data": "[dataset_object]"
}

### Response
#### Success Response (200)
- **pred** (DataFrame) - The predicted values from the model.

#### Response Example
{
  "pred": "[predicted_dataframe]"
}
```

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

### Fit and Predict SEM Model

Source: https://gitlab.com/georgy.m/semopy/-/blob/master/notebooks/semopy - Walkthrough.ipynb

Fits a structural equation model (SEM) using the provided data and then generates predictions based on the fitted model. It also calculates and prints the mean relative error between the predictions and the true values, highlighting potential issues with imputation methods.

```python
m.fit(data)
pred = m.predict(data)
print('Mean relative error: {:.3f}%'.format(
       abs((pred.values[mask_x, mask_y] - data_true) / data_true).mean() * 100))
```

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

### Calculate SEM Model Fit Statistics

Source: https://gitlab.com/georgy.m/semopy/-/blob/master/notebooks/semopy - Walkthrough.ipynb

Calculates and displays a comprehensive set of fit indices for a structural equation model (SEM). These indices help researchers evaluate the overall fit of the model to the data.

```python
from semopy import calc_stats
calc_stats(m)
```

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

### Perform Multi-Group Analysis with Semopy

Source: https://context7.com/georgy.m/semopy/llms.txt

The multigroup() function in semopy enables multi-group Structural Equation Modeling (SEM) analysis. It fits a specified model to different groups within the data and facilitates comparison of estimates across these groups. The function supports both identical and group-specific model definitions.

```python
from semopy import multigroup, Model
from semopy.examples import holzinger39
import pandas as pd

data = holzinger39.get_data()
desc = holzinger39.get_model()

result = multigroup(desc, data, group='school')
print(result)

print("\nEstimates for Pasteur school:")
print(result.estimates['Pasteur'])

print("\nEstimates for Grant-White school:")
print(result.estimates['Grant-White'])

for group in result.groups:
    print(f"\n{group}:")
    print(result.stats[group])

desc_pasteur = """
visual =~ x1 + x2 + x3
textual =~ x4 + x5 + x6
speed =~ x7 + x8 + x9
visual ~~ textual
"""

desc_grantwhite = """
visual =~ x1 + x2 + x3
textual =~ x4 + x5 + x6
speed =~ x7 + x8 + x9
visual ~~ speed
"""

group_models = {
    'Pasteur': desc_pasteur,
    'Grant-White': desc_grantwhite
}

result_diff = multigroup(group_models, data, group='school')
print("\nDifferent models per group:")
print(result_diff)
```

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

### Evaluating ModelEffects Performance

Source: https://gitlab.com/georgy.m/semopy/-/blob/master/notebooks/semopy - Walkthrough.ipynb

Fits a model using ModelEffects with a provided covariance matrix for random effects. This demonstrates improved estimation accuracy over standard ModelMeans.

```python
m = ModelEffects(desc)
m.fit(data, group='group', k=k)
ins = m.inspect()
errs = list()
for _, row in params.iterrows():
    t = (ins['op'] == row['op']) & (ins['lval'] == row['lval']) &\
        (ins['rval'] == row['rval'])
    t = ins[t]
    est = t['Estimate'].values[0]
    errs.append(abs((est - row['est']) / row['est']))
err = np.mean(errs)
print("Mean relative error: {:.3f}%".format(err * 100))
```

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

### Calculate Robust Standard Errors with Semopy

Source: https://gitlab.com/georgy.m/semopy/-/blob/master/notebooks/semopy - Walkthrough.ipynb

This snippet demonstrates how to apply Huber-White correction to standard errors estimation using the `inspect` method with `se_robust=True`. It takes a fitted semopy model and returns a table with robust standard errors, z-values, and p-values.

```python
desc = political_democracy.get_model()
data = political_democracy.get_data()
m = Model(desc)
m.fit(data)
robust = m.inspect(se_robust=True)
robust
```

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

### Calculate SEM Model Fit Indices

Source: https://context7.com/georgy.m/semopy/llms.txt

Computes comprehensive fit indices for a fitted SEMopy model. Returns a DataFrame containing metrics like Chi-square, CFI, RMSEA, and AIC for model evaluation.

```python
from semopy import calc_stats
stats = calc_stats(model)
print(stats.T)
print(f"CFI: {stats['CFI'].values[0]:.3f}")
```

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

### Estimate Factor Scores using Semopy's predict_factors

Source: https://context7.com/georgy.m/semopy/llms.txt

The predict_factors() method in semopy estimates latent factor scores for individual observations using the Maximum A Posteriori (MAP) approach. These scores can be centered or uncentered and are useful for subsequent analyses, such as correlations or regressions.

```python
from semopy import Model
from semopy.examples import holzinger39
import pandas as pd
import numpy as np

desc = holzinger39.get_model()
data = holzinger39.get_data()

model = Model(desc)
model.fit(data)

factor_scores = model.predict_factors(data)
print("Estimated factor scores:")
print(factor_scores.head(10))

factor_scores_uncentered = model.predict_factors(data, center=False)
print(f"\nUncentered factor means:")
print(factor_scores_uncentered.mean())

print("\nFactor correlations:")
print(factor_scores.corr())

data_with_factors = pd.concat([data.reset_index(drop=True), factor_scores], axis=1)
print("\nData with factor scores:")
print(data_with_factors[['x1', 'x2', 'x3', 'visual', 'textual', 'speed']].head())

import scipy.stats as stats
visual_scores = factor_scores['visual']
external_var = np.random.normal(0, 1, len(visual_scores))
r, p = stats.pearsonr(visual_scores, external_var)
print(f"\nCorrelation with external variable: r={r:.3f}, p={p:.3f}")
```

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