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        "description": "# PLSPM: A library implementing Partial Least Squares Path Modeling [![PyPI version](https://badge.fury.io/py/plspm.svg)](https://badge.fury.io/py/plspm)\n\n_Please note: This is not an officially supported Google product._\n\n**plspm** is a Python 3 package dedicated to Partial Least Squares Path Modeling (PLS-PM) analysis. It is a port of the R package [plspm](https://github.com/gastonstat/plspm), with additional features adopted from the R package [seminr](https://github.com/sem-in-r/seminr)\n\nPLSPM (partial least squares path modeling) is a correlation-based structural equation modeling (SEM) algorithm. It allows for estimation of complex cause-effect or prediction models using latent/manifest variables. \n\nPLSPM may be preferred to other SEM methods for several reasons: it is a method that is appropriate for exploratory research, can be used with small-to-medium sample sizes (as well as large data sets), and does not require assumptions of multivariate normality. (See Hulland, J. (1999). Use of partial least squares (PLS) in strategic management research: a review of four recent studies. Strategic management journal, 20(2), 195-204.) In contrast to covariance-based SEM (CBSEM), goodness of fit is less important, because the purpose of the algorithm is to optimize for prediction of the dependent variable vs. fit of data to a predetermined model. (See \"goodness of fit\" vs \"goodness of model\" in Chin, W. W. (2010). How to write up and report PLS analyses. In Handbook of partial least squares (pp. 655-690). Springer, Berlin, Heidelberg.)\n\n### Features\n\n* Uses variance-based PLS esimation to model composite constructs using Mode A and Mode B\n* Uses a natural-feeling, domain specific language to build and estimate structural equation models, including second-order constructs\n* Supports centroid, factorial, and path schemes\n* Supports metric and non-metric numerical data (including nominal and ordinal)\n* Handles missing data\n* Bootstrapping with multi-core support\n* Tested against [seminr](https://github.com/sem-in-r/seminr), which is, in turn, tested against SmartPLS (Ringle et al., 2015) and ADANCO (Henseler and Dijkstra, 2015), as well as other R packages such as semPLS (Monecke and Leisch, 2012) and matrixpls (R\u00f6nkk\u00f6, 2016).\n\n### Planned but not yet implemented\n\n* Native modeling of moderation\n* Improved assessment measures such as HTMT, VIF, f^2, Q^2, and q^2\n* Modeling formative constructs using the PLS consistent (PLSc) algorithm\n\n## Installation\nYou can install the latest version of this package using pip:\n\n```sh\npython3 -m pip install --user plspm\n```\n\nIt's hosted on pypi: https://pypi.org/project/plspm/\n\n## Use\n\nplspm expects to get a Pandas DataFrame containing your data. You start by creating a [Config](https://plspm.readthedocs.io/en/latest/source/plspm.config.html) object with the details of the model, and then pass it, along with the data and optionally some further configuration, to an instance of [Plspm](https://plspm.readthedocs.io/en/latest/source/plspm.plspm.html). Use the examples below to get started, or browse the [documentation](https://plspm.readthedocs.io/) (start with [Config](https://plspm.readthedocs.io/en/latest/source/plspm.config.html) and [Plspm](https://plspm.readthedocs.io/en/latest/source/plspm.plspm.html))\n\n## Examples\n\n### PLS-PM with metric data\n\nTypical example with a Customer Satisfaction Model\n\n```py\n#!/usr/bin/env python3\nimport pandas as pd, plspm.config as c\nfrom plspm.plspm import Plspm\nfrom plspm.scheme import Scheme\nfrom plspm.mode import Mode\n\nsatisfaction = pd.read_csv(\"file:tests/data/satisfaction.csv\", index_col=0)\n\nstructure = c.Structure()\nstructure.add_path([\"IMAG\"], [\"EXPE\", \"SAT\", \"LOY\"])\nstructure.add_path([\"EXPE\"], [\"QUAL\", \"VAL\", \"SAT\"])\nstructure.add_path([\"QUAL\"], [\"VAL\", \"SAT\"])\nstructure.add_path([\"VAL\"], [\"SAT\"])\nstructure.add_path([\"SAT\"], [\"LOY\"])\n\nconfig = c.Config(structure.path(), scaled=False)\nconfig.add_lv_with_columns_named(\"IMAG\", Mode.A, satisfaction, \"imag\")\nconfig.add_lv_with_columns_named(\"EXPE\", Mode.A, satisfaction, \"expe\")\nconfig.add_lv_with_columns_named(\"QUAL\", Mode.A, satisfaction, \"qual\")\nconfig.add_lv_with_columns_named(\"VAL\", Mode.A, satisfaction, \"val\")\nconfig.add_lv_with_columns_named(\"SAT\", Mode.A, satisfaction, \"sat\")\nconfig.add_lv_with_columns_named(\"LOY\", Mode.A, satisfaction, \"loy\")\n\nplspm_calc = Plspm(satisfaction, config, Scheme.CENTROID)\nprint(plspm_calc.inner_summary())\nprint(plspm_calc.path_coefficients())\n```\n\nThis will produce the output:\n```\n            type  r_squared  block_communality  mean_redundancy       ave\nEXPE  Endogenous   0.335194           0.616420         0.206620  0.616420\nIMAG   Exogenous   0.000000           0.582269         0.000000  0.582269\nLOY   Endogenous   0.509923           0.639052         0.325867  0.639052\nQUAL  Endogenous   0.719688           0.658572         0.473966  0.658572\nSAT   Endogenous   0.707321           0.758891         0.536779  0.758891\nVAL   Endogenous   0.590084           0.664416         0.392061  0.664416\n\n          IMAG      EXPE      QUAL       VAL       SAT  LOY\nIMAG  0.000000  0.000000  0.000000  0.000000  0.000000    0\nEXPE  0.578959  0.000000  0.000000  0.000000  0.000000    0\nQUAL  0.000000  0.848344  0.000000  0.000000  0.000000    0\nVAL   0.000000  0.105478  0.676656  0.000000  0.000000    0\nSAT   0.200724 -0.002754  0.122145  0.589331  0.000000    0\nLOY   0.275150  0.000000  0.000000  0.000000  0.495479    0\n```\n\n### Specifying higher-order constructs\n\nExample using [seminr](https://github.com/sem-in-r/seminr)'s mobile industry data set:\n\n```py\nmobi = pd.read_csv(\"file:tests/data/mobi.csv\", index_col=0)\n\nstructure = c.Structure()\nstructure.add_path([\"Expectation\", \"Quality\"], [\"Satisfaction\"])\nstructure.add_path([\"Satisfaction\"], [\"Complaints\", \"Loyalty\"])\n\nconfig = c.Config(structure.path(), default_scale=Scale.NUM)\nconfig.add_higher_order(\"Satisfaction\", Mode.A, [\"Image\", \"Value\"])\nconfig.add_lv_with_columns_named(\"Expectation\", Mode.A, mobi, \"CUEX\")\nconfig.add_lv_with_columns_named(\"Quality\", Mode.B, mobi, \"PERQ\")\nconfig.add_lv_with_columns_named(\"Loyalty\", Mode.A, mobi, \"CUSL\")\nconfig.add_lv_with_columns_named(\"Image\", Mode.A, mobi, \"IMAG\")\nconfig.add_lv_with_columns_named(\"Complaints\", Mode.A, mobi, \"CUSCO\")\nconfig.add_lv_with_columns_named(\"Value\", Mode.A, mobi, \"PERV\")\n\nmobi_pls = Plspm(mobi, config, Scheme.PATH, 100, 0.00000001)\n\nprint(plspm_calc.inner_model())\n```\n\nThis will produce the output:\n```\n                                     from            to  estimate  std error          t         p>|t|\nindex                                                                                                \nQuality -> Satisfaction           Quality  Satisfaction  0.743041   0.046318  16.042102  3.633866e-40\nExpectation -> Satisfaction   Expectation  Satisfaction  0.089572   0.046318   1.933832  5.427626e-02\nSatisfaction -> Loyalty      Satisfaction       Loyalty  0.627940   0.049420  12.706272  7.996788e-29\nSatisfaction -> Complaints   Satisfaction    Complaints  0.486696   0.055472   8.773752  2.841768e-16\n```\n\n### PLS-PM with nonmetric data\n\nExample with the classic Russett data (original data set)\n\n```py\n#!/usr/bin/env python3\nimport pandas as pd, plspm.config as c\nfrom plspm.plspm import Plspm\nfrom plspm.scale import Scale\nfrom plspm.scheme import Scheme\nfrom plspm.mode import Mode\n\nrussa = pd.read_csv(\"file:tests/data/russa.csv\", index_col=0)\n\nstructure = c.Structure()\nstructure.add_path([\"AGRI\", \"IND\"], [\"POLINS\"])\n\nconfig = c.Config(structure.path(), default_scale=Scale.NUM)\nconfig.add_lv(\"AGRI\", Mode.A, c.MV(\"gini\"), c.MV(\"farm\"), c.MV(\"rent\"))\nconfig.add_lv(\"IND\", Mode.A, c.MV(\"gnpr\"), c.MV(\"labo\"))\nconfig.add_lv(\"POLINS\", Mode.A, c.MV(\"ecks\"), c.MV(\"death\"), c.MV(\"demo\"), c.MV(\"inst\"))\n\nplspm_calc = Plspm(russa, config, Scheme.CENTROID, 100, 0.0000001)\nprint(plspm_calc.inner_summary())\nprint(plspm_calc.effects())\n```\n\nThis will produce the output:\n```\n              type  r_squared  block_communality  mean_redundancy       ave\nAGRI     Exogenous   0.000000           0.739560         0.000000  0.739560\nIND      Exogenous   0.000000           0.907524         0.000000  0.907524\nPOLINS  Endogenous   0.592258           0.565175         0.334729  0.565175\n\n   from      to    direct  indirect     total\n0  AGRI  POLINS  0.225639       0.0  0.225639\n1   IND  POLINS  0.671457       0.0  0.671457\n```\n\n#### Example 2: Different Scaling\n\nPLS-PM using data set `russa`, and different scaling\n\n```py\n#!/usr/bin/python3\nimport pandas as pd, plspm.config as c, plspm.util as util\nfrom plspm.plspm import Plspm\nfrom plspm.scale import Scale\nfrom plspm.scheme import Scheme\nfrom plspm.mode import Mode\n\nrussa = pd.read_csv(\"file:tests/data/russa.csv\", index_col=0)\n\nstructure = c.Structure()\nstructure.add_path([\"AGRI\", \"IND\"], [\"POLINS\"])\nconfig = c.Config(structure.path(), default_scale=Scale.NUM)\nconfig.add_lv(\"AGRI\", Mode.A, c.MV(\"gini\"), c.MV(\"farm\"), c.MV(\"rent\"))\nconfig.add_lv(\"IND\", Mode.A, c.MV(\"gnpr\", Scale.ORD), c.MV(\"labo\", Scale.ORD))\nconfig.add_lv(\"POLINS\", Mode.A, c.MV(\"ecks\"), c.MV(\"death\"), c.MV(\"demo\", Scale.NOM), c.MV(\"inst\"))\n\nplspm_calc = Plspm(russa, config, Scheme.CENTROID, 100, 0.0000001)\n```\n\n#### Example 3: Missing Data\n\n```py\n#!/usr/bin/env python3\nimport pandas as pd, plspm.config as c\nfrom plspm.plspm import Plspm\nfrom plspm.scale import Scale\nfrom plspm.scheme import Scheme\nfrom plspm.mode import Mode\n\nrussa = pd.read_csv(\"file:tests/data/russa.csv\", index_col=0)\nrussa.iloc[0, 0] = np.NaN\nrussa.iloc[3, 3] = np.NaN\nrussa.iloc[5, 5] = np.NaN\n\nstructure = c.Structure()\nstructure.add_path([\"AGRI\", \"IND\"], [\"POLINS\"])\nconfig = c.Config(structure.path(), default_scale=Scale.NUM)\nconfig.add_lv(\"AGRI\", Mode.A, c.MV(\"gini\"), c.MV(\"farm\"), c.MV(\"rent\"))\nconfig.add_lv(\"IND\", Mode.A, c.MV(\"gnpr\"), c.MV(\"labo\"))\nconfig.add_lv(\"POLINS\", Mode.A, c.MV(\"ecks\"), c.MV(\"death\"), c.MV(\"demo\"), c.MV(\"inst\"))\n\nplspm_calc = Plspm(russa, config, Scheme.CENTROID, 100, 0.0000001)\n```\n\n## Maintainers\n\n[Jez Humble](https://continuousdelivery.com/)\n  (`humble at google.com`)\n\n[Nicole Forsgren](https://nicolefv.com/)\n  (`nicolefv at google.com`)\n\n\n",
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