diff --git a/examples/case_studies/CFA_SEM.ipynb b/examples/case_studies/CFA_SEM.ipynb new file mode 100644 index 000000000..4922dae8e --- /dev/null +++ b/examples/case_studies/CFA_SEM.ipynb @@ -0,0 +1,7988 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "(cfa_sem_notebook)=\n", + "# Confirmatory Factor Analysis and Structural Equation Models in Psychometrics\n", + "\n", + ":::{post} September, 2024\n", + ":tags: cfa, sem, regression, \n", + ":category: intermediate, reference\n", + ":author: Nathaniel Forde\n", + ":::" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "> \"Evidently, the notions of relevance and dependence are far more basic to human reasoning than the numerical values attached to probability judgments...the language used for representing probabilistic information should allow assertions about dependency relationships to be expressed qualitatively, directly, and explicitly\" - Pearl in _Probabilistic Reasoning in Intelligent Systems_ {cite:t}`pearl1985prob`\n", + "\n", + "Measurement data is psychometrics is often derived from a strategically constructed survey aimed at a particular target phenomena. Some intuited, but not yet measured, concept that arguably plays a determining role in human action, motivation or sentiment. The relative “fuzziness” of the subject matter in psychometrics has had a catalyzing effect on the methodological rigour sought in the science. \n", + "\n", + "Survey designs are agonized over for correct tone and rhythm of sentence structure. Measurement scales are doubly checked for reliability and correctness. The literature is consulted and questions are refined. Analysis steps are justified and tested under a wealth of modelling routines. Model architectures are defined and refined to better express the hypothesized structures in the data-generating process. We will see how such due diligence leads to powerful and expressive models that grant us tractability on thorny questions of human affect. \n", + "\n", + "Throughout we draw on Roy Levy and Robert J. Mislevy's excellent _Bayesian Psychometric Modeling_. " + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import warnings\n", + "\n", + "import arviz as az\n", + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "import pandas as pd\n", + "import pymc as pm\n", + "import pytensor.tensor as pt\n", + "import seaborn as sns\n", + "\n", + "warnings.filterwarnings(\"ignore\", category=RuntimeWarning)\n", + "warnings.filterwarnings(\"ignore\", category=UserWarning)" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "%config InlineBackend.figure_format = 'retina' # high resolution figures\n", + "az.style.use(\"arviz-darkgrid\")\n", + "rng = np.random.default_rng(42)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Latent Constructs and Measurement\n", + "\n", + "Our data is borrowed from work by Boris Mayer and Andrew Ellis found [here](https://methodenlehre.github.io/SGSCLM-R-course/cfa-and-sem-with-lavaan.html#structural-equation-modelling-sem). They demonstrate CFA and SEM modelling with lavaan.\n", + "\n", + "We have survey responses from ~300 individuals who have answered questions regarding their upbringing, self-efficacy and reported life-satisfaction. The hypothetical dependency structure in this life-satisfaction dataset posits a moderated relationship between scores related to life-satisfaction, parental and family support and self-efficacy. It is not a trivial task to be able to design a survey that can elicit answers plausibly mapped to each of these “factors” or themes, never mind finding a model of their relationship that can inform us as to the relative of impact of each on life-satisfaction outcomes.\n", + "\n", + "First let's pull out the data and examine some summary statistics." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
\n", + " | ID | \n", + "region | \n", + "gender | \n", + "age | \n", + "se_acad_p1 | \n", + "se_acad_p2 | \n", + "se_acad_p3 | \n", + "se_social_p1 | \n", + "se_social_p2 | \n", + "se_social_p3 | \n", + "sup_friends_p1 | \n", + "sup_friends_p2 | \n", + "sup_friends_p3 | \n", + "sup_parents_p1 | \n", + "sup_parents_p2 | \n", + "sup_parents_p3 | \n", + "ls_p1 | \n", + "ls_p2 | \n", + "ls_p3 | \n", + "
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0 | \n", + "1 | \n", + "west | \n", + "female | \n", + "13 | \n", + "4.857143 | \n", + "5.571429 | \n", + "4.500000 | \n", + "5.80 | \n", + "5.500000 | \n", + "5.40 | \n", + "6.5 | \n", + "6.5 | \n", + "7.0 | \n", + "7.0 | \n", + "7.0 | \n", + "6.0 | \n", + "5.333333 | \n", + "6.75 | \n", + "5.50 | \n", + "
1 | \n", + "2 | \n", + "west | \n", + "male | \n", + "14 | \n", + "4.571429 | \n", + "4.285714 | \n", + "4.666667 | \n", + "5.00 | \n", + "5.500000 | \n", + "4.80 | \n", + "4.5 | \n", + "4.5 | \n", + "5.5 | \n", + "5.0 | \n", + "6.0 | \n", + "4.5 | \n", + "4.333333 | \n", + "5.00 | \n", + "4.50 | \n", + "
2 | \n", + "10 | \n", + "west | \n", + "female | \n", + "14 | \n", + "4.142857 | \n", + "6.142857 | \n", + "5.333333 | \n", + "5.20 | \n", + "4.666667 | \n", + "6.00 | \n", + "4.0 | \n", + "4.5 | \n", + "3.5 | \n", + "7.0 | \n", + "7.0 | \n", + "6.5 | \n", + "6.333333 | \n", + "5.50 | \n", + "4.00 | \n", + "
3 | \n", + "11 | \n", + "west | \n", + "female | \n", + "14 | \n", + "5.000000 | \n", + "5.428571 | \n", + "4.833333 | \n", + "6.40 | \n", + "5.833333 | \n", + "6.40 | \n", + "7.0 | \n", + "7.0 | \n", + "7.0 | \n", + "7.0 | \n", + "7.0 | \n", + "7.0 | \n", + "4.333333 | \n", + "6.50 | \n", + "6.25 | \n", + "
4 | \n", + "12 | \n", + "west | \n", + "female | \n", + "14 | \n", + "5.166667 | \n", + "5.600000 | \n", + "4.800000 | \n", + "5.25 | \n", + "5.400000 | \n", + "5.25 | \n", + "7.0 | \n", + "7.0 | \n", + "7.0 | \n", + "6.5 | \n", + "6.5 | \n", + "7.0 | \n", + "5.666667 | \n", + "6.00 | \n", + "5.75 | \n", + "
\n", + " | mean | \n", + "sd | \n", + "hdi_3% | \n", + "hdi_97% | \n", + "mcse_mean | \n", + "mcse_sd | \n", + "ess_bulk | \n", + "ess_tail | \n", + "r_hat | \n", + "
---|---|---|---|---|---|---|---|---|---|
lambdas1[se_social_p1] | \n", + "1.000 | \n", + "0.000 | \n", + "1.000 | \n", + "1.000 | \n", + "0.000 | \n", + "0.000 | \n", + "4000.0 | \n", + "4000.0 | \n", + "NaN | \n", + "
lambdas1[se_social_p2] | \n", + "0.977 | \n", + "0.060 | \n", + "0.863 | \n", + "1.089 | \n", + "0.002 | \n", + "0.001 | \n", + "993.0 | \n", + "1688.0 | \n", + "1.0 | \n", + "
lambdas1[se_social_p3] | \n", + "0.947 | \n", + "0.074 | \n", + "0.810 | \n", + "1.091 | \n", + "0.002 | \n", + "0.002 | \n", + "1110.0 | \n", + "1965.0 | \n", + "1.0 | \n", + "
lambdas2[ls_p1] | \n", + "1.000 | \n", + "0.000 | \n", + "1.000 | \n", + "1.000 | \n", + "0.000 | \n", + "0.000 | \n", + "4000.0 | \n", + "4000.0 | \n", + "NaN | \n", + "
lambdas2[ls_p2] | \n", + "0.815 | \n", + "0.087 | \n", + "0.672 | \n", + "0.989 | \n", + "0.004 | \n", + "0.003 | \n", + "524.0 | \n", + "792.0 | \n", + "1.0 | \n", + "
lambdas2[ls_p3] | \n", + "0.861 | \n", + "0.095 | \n", + "0.689 | \n", + "1.047 | \n", + "0.004 | \n", + "0.003 | \n", + "713.0 | \n", + "1164.0 | \n", + "1.0 | \n", + "
<xarray.Dataset>\n", + "Dimensions: (chain: 4, draw: 1000, indicators_1: 3,\n", + " indicators_2: 3, obs: 283, latent: 2, indicators: 6,\n", + " chol_cov_dim_0: 3, chol_cov_corr_dim_0: 2,\n", + " chol_cov_corr_dim_1: 2, chol_cov_stds_dim_0: 2,\n", + " mu_dim_0: 283, mu_dim_1: 6)\n", + "Coordinates: (12/13)\n", + " * chain (chain) int64 0 1 2 3\n", + " * draw (draw) int64 0 1 2 3 4 5 6 ... 994 995 996 997 998 999\n", + " * indicators_1 (indicators_1) <U12 'se_social_p1' ... 'se_social_p3'\n", + " * indicators_2 (indicators_2) <U5 'ls_p1' 'ls_p2' 'ls_p3'\n", + " * obs (obs) int64 0 1 2 3 4 5 6 ... 277 278 279 280 281 282\n", + " * latent (latent) <U6 'SE_SOC' 'LS'\n", + " ... ...\n", + " * chol_cov_dim_0 (chol_cov_dim_0) int64 0 1 2\n", + " * chol_cov_corr_dim_0 (chol_cov_corr_dim_0) int64 0 1\n", + " * chol_cov_corr_dim_1 (chol_cov_corr_dim_1) int64 0 1\n", + " * chol_cov_stds_dim_0 (chol_cov_stds_dim_0) int64 0 1\n", + " * mu_dim_0 (mu_dim_0) int64 0 1 2 3 4 5 ... 278 279 280 281 282\n", + " * mu_dim_1 (mu_dim_1) int64 0 1 2 3 4 5\n", + "Data variables:\n", + " lambdas_1 (chain, draw, indicators_1) float64 -1.601 ... 0.962\n", + " lambdas_2 (chain, draw, indicators_2) float64 11.47 ... 0.7527\n", + " ksi (chain, draw, obs, latent) float64 0.4271 ... 0.9507\n", + " tau (chain, draw, indicators) float64 5.301 5.437 ... 5.233\n", + " chol_cov (chain, draw, chol_cov_dim_0) float64 0.6359 ... 0.5823\n", + " Psi (chain, draw, indicators) float64 0.4654 ... 0.6677\n", + " lambdas1 (chain, draw, indicators_1) float64 1.0 ... 0.962\n", + " lambdas2 (chain, draw, indicators_2) float64 1.0 ... 0.7527\n", + " chol_cov_corr (chain, draw, chol_cov_corr_dim_0, chol_cov_corr_dim_1) float64 ...\n", + " chol_cov_stds (chain, draw, chol_cov_stds_dim_0) float64 0.6359 .....\n", + " mu (chain, draw, mu_dim_0, mu_dim_1) float64 5.728 ... ...\n", + "Attributes:\n", + " created_at: 2024-09-25T11:16:42.786789\n", + " arviz_version: 0.17.0
<xarray.Dataset>\n", + "Dimensions: (chain: 4, draw: 1000, likelihood_dim_2: 283,\n", + " likelihood_dim_3: 6)\n", + "Coordinates:\n", + " * chain (chain) int64 0 1 2 3\n", + " * draw (draw) int64 0 1 2 3 4 5 6 ... 993 994 995 996 997 998 999\n", + " * likelihood_dim_2 (likelihood_dim_2) int64 0 1 2 3 4 ... 278 279 280 281 282\n", + " * likelihood_dim_3 (likelihood_dim_3) int64 0 1 2 3 4 5\n", + "Data variables:\n", + " likelihood (chain, draw, likelihood_dim_2, likelihood_dim_3) float64 ...\n", + "Attributes:\n", + " created_at: 2024-09-25T11:16:43.032825\n", + " arviz_version: 0.17.0\n", + " inference_library: pymc\n", + " inference_library_version: 5.10.3
<xarray.Dataset>\n", + "Dimensions: (chain: 4, draw: 1000, likelihood_dim_0: 283,\n", + " likelihood_dim_1: 6)\n", + "Coordinates:\n", + " * chain (chain) int64 0 1 2 3\n", + " * draw (draw) int64 0 1 2 3 4 5 6 ... 993 994 995 996 997 998 999\n", + " * likelihood_dim_0 (likelihood_dim_0) int64 0 1 2 3 4 ... 278 279 280 281 282\n", + " * likelihood_dim_1 (likelihood_dim_1) int64 0 1 2 3 4 5\n", + "Data variables:\n", + " likelihood (chain, draw, likelihood_dim_0, likelihood_dim_1) float64 ...\n", + "Attributes:\n", + " created_at: 2024-09-25T11:16:42.790979\n", + " arviz_version: 0.17.0
<xarray.Dataset>\n", + "Dimensions: (chain: 4, draw: 1000)\n", + "Coordinates:\n", + " * chain (chain) int64 0 1 2 3\n", + " * draw (draw) int64 0 1 2 3 4 5 6 ... 993 994 995 996 997 998 999\n", + "Data variables:\n", + " acceptance_rate (chain, draw) float64 0.9026 0.9604 0.9726 ... 0.992 0.9294\n", + " step_size (chain, draw) float64 0.1464 0.1464 ... 0.1427 0.1427\n", + " diverging (chain, draw) bool False False False ... False False False\n", + " energy (chain, draw) float64 2.091e+03 2.111e+03 ... 2.072e+03\n", + " n_steps (chain, draw) int64 31 31 31 31 31 31 ... 31 31 31 31 31 31\n", + " tree_depth (chain, draw) int64 5 5 5 5 5 5 5 5 5 ... 5 5 5 5 5 5 5 5 5\n", + " lp (chain, draw) float64 1.803e+03 1.804e+03 ... 1.78e+03\n", + "Attributes:\n", + " created_at: 2024-09-25T11:16:42.789976\n", + " arviz_version: 0.17.0
<xarray.Dataset>\n", + "Dimensions: (likelihood_dim_0: 283, likelihood_dim_1: 6)\n", + "Coordinates:\n", + " * likelihood_dim_0 (likelihood_dim_0) int64 0 1 2 3 4 ... 278 279 280 281 282\n", + " * likelihood_dim_1 (likelihood_dim_1) int64 0 1 2 3 4 5\n", + "Data variables:\n", + " likelihood (likelihood_dim_0, likelihood_dim_1) float64 5.8 ... 5.75\n", + "Attributes:\n", + " created_at: 2024-09-25T11:16:42.791317\n", + " arviz_version: 0.17.0\n", + " inference_library: numpyro\n", + " inference_library_version: 0.13.2\n", + " sampling_time: 4.970539
\n", + " | mean | \n", + "sd | \n", + "hdi_3% | \n", + "hdi_97% | \n", + "mcse_mean | \n", + "mcse_sd | \n", + "ess_bulk | \n", + "ess_tail | \n", + "r_hat | \n", + "
---|---|---|---|---|---|---|---|---|---|
lambdas1[se_social_p1] | \n", + "1.000 | \n", + "0.000 | \n", + "1.000 | \n", + "1.000 | \n", + "0.000 | \n", + "0.000 | \n", + "40000.0 | \n", + "40000.0 | \n", + "NaN | \n", + "
lambdas1[se_social_p2] | \n", + "0.928 | \n", + "0.128 | \n", + "0.694 | \n", + "1.172 | \n", + "0.002 | \n", + "0.002 | \n", + "3090.0 | \n", + "5423.0 | \n", + "1.0 | \n", + "
lambdas1[se_social_p3] | \n", + "0.854 | \n", + "0.139 | \n", + "0.598 | \n", + "1.121 | \n", + "0.002 | \n", + "0.002 | \n", + "4600.0 | \n", + "8366.0 | \n", + "1.0 | \n", + "
lambdas1[sup_parents_p1] | \n", + "2.321 | \n", + "0.289 | \n", + "1.807 | \n", + "2.867 | \n", + "0.008 | \n", + "0.005 | \n", + "1421.0 | \n", + "2736.0 | \n", + "1.0 | \n", + "
lambdas1[sup_parents_p2] | \n", + "2.171 | \n", + "0.278 | \n", + "1.684 | \n", + "2.699 | \n", + "0.008 | \n", + "0.005 | \n", + "1333.0 | \n", + "2592.0 | \n", + "1.0 | \n", + "
lambdas1[sup_parents_p3] | \n", + "2.334 | \n", + "0.290 | \n", + "1.832 | \n", + "2.898 | \n", + "0.008 | \n", + "0.005 | \n", + "1442.0 | \n", + "2795.0 | \n", + "1.0 | \n", + "
lambdas2[ls_p1] | \n", + "1.000 | \n", + "0.000 | \n", + "1.000 | \n", + "1.000 | \n", + "0.000 | \n", + "0.000 | \n", + "40000.0 | \n", + "40000.0 | \n", + "NaN | \n", + "
lambdas2[ls_p2] | \n", + "0.777 | \n", + "0.105 | \n", + "0.589 | \n", + "0.975 | \n", + "0.002 | \n", + "0.002 | \n", + "2530.0 | \n", + "4296.0 | \n", + "1.0 | \n", + "
lambdas2[ls_p3] | \n", + "1.080 | \n", + "0.135 | \n", + "0.840 | \n", + "1.335 | \n", + "0.003 | \n", + "0.002 | \n", + "2271.0 | \n", + "3902.0 | \n", + "1.0 | \n", + "
\n", + " | factor_loading | \n", + "factor_loading_weight | \n", + "factor | \n", + "factor_loading_weight_sq | \n", + "sum_sq_loadings | \n", + "error_variances | \n", + "total_indicator_variance | \n", + "total_variance | \n", + "indicator_explained_variance | \n", + "factor_explained_variance | \n", + "
---|---|---|---|---|---|---|---|---|---|---|
0 | \n", + "lambdas1[se_acad_p1] | \n", + "1.00 | \n", + "lambdas1 | \n", + "1.00 | \n", + "2.61 | \n", + "0.41 | \n", + "1.41 | \n", + "21.47 | \n", + "0.05 | \n", + "0.12 | \n", + "
1 | \n", + "lambdas1[se_acad_p2] | \n", + "0.82 | \n", + "lambdas1 | \n", + "0.67 | \n", + "2.61 | \n", + "0.41 | \n", + "1.09 | \n", + "21.47 | \n", + "0.03 | \n", + "0.12 | \n", + "
2 | \n", + "lambdas1[se_acad_p3] | \n", + "0.97 | \n", + "lambdas1 | \n", + "0.94 | \n", + "2.61 | \n", + "0.47 | \n", + "1.41 | \n", + "21.47 | \n", + "0.04 | \n", + "0.12 | \n", + "
3 | \n", + "lambdas2[se_social_p1] | \n", + "1.00 | \n", + "lambdas2 | \n", + "1.00 | \n", + "2.81 | \n", + "0.43 | \n", + "1.43 | \n", + "21.47 | \n", + "0.05 | \n", + "0.13 | \n", + "
4 | \n", + "lambdas2[se_social_p2] | \n", + "0.96 | \n", + "lambdas2 | \n", + "0.92 | \n", + "2.81 | \n", + "0.36 | \n", + "1.29 | \n", + "21.47 | \n", + "0.04 | \n", + "0.13 | \n", + "
5 | \n", + "lambdas2[se_social_p3] | \n", + "0.94 | \n", + "lambdas2 | \n", + "0.88 | \n", + "2.81 | \n", + "0.55 | \n", + "1.43 | \n", + "21.47 | \n", + "0.04 | \n", + "0.13 | \n", + "
6 | \n", + "lambdas3[sup_friends_p1] | \n", + "1.00 | \n", + "lambdas3 | \n", + "1.00 | \n", + "2.46 | \n", + "0.52 | \n", + "1.52 | \n", + "21.47 | \n", + "0.05 | \n", + "0.11 | \n", + "
7 | \n", + "lambdas3[sup_friends_p2] | \n", + "0.80 | \n", + "lambdas3 | \n", + "0.64 | \n", + "2.46 | \n", + "0.51 | \n", + "1.15 | \n", + "21.47 | \n", + "0.03 | \n", + "0.11 | \n", + "
8 | \n", + "lambdas3[sup_friends_p3] | \n", + "0.91 | \n", + "lambdas3 | \n", + "0.82 | \n", + "2.46 | \n", + "0.62 | \n", + "1.44 | \n", + "21.47 | \n", + "0.04 | \n", + "0.11 | \n", + "
9 | \n", + "lambdas4[sup_parents_p1] | \n", + "1.00 | \n", + "lambdas4 | \n", + "1.00 | \n", + "3.11 | \n", + "0.55 | \n", + "1.55 | \n", + "21.47 | \n", + "0.05 | \n", + "0.14 | \n", + "
10 | \n", + "lambdas4[sup_parents_p2] | \n", + "1.04 | \n", + "lambdas4 | \n", + "1.08 | \n", + "3.11 | \n", + "0.54 | \n", + "1.62 | \n", + "21.47 | \n", + "0.05 | \n", + "0.14 | \n", + "
11 | \n", + "lambdas4[sup_parents_p3] | \n", + "1.01 | \n", + "lambdas4 | \n", + "1.02 | \n", + "3.11 | \n", + "0.68 | \n", + "1.70 | \n", + "21.47 | \n", + "0.05 | \n", + "0.14 | \n", + "
12 | \n", + "lambdas5[ls_p1] | \n", + "1.00 | \n", + "lambdas5 | \n", + "1.00 | \n", + "2.61 | \n", + "0.67 | \n", + "1.67 | \n", + "21.47 | \n", + "0.05 | \n", + "0.12 | \n", + "
13 | \n", + "lambdas5[ls_p2] | \n", + "0.79 | \n", + "lambdas5 | \n", + "0.63 | \n", + "2.61 | \n", + "0.53 | \n", + "1.16 | \n", + "21.47 | \n", + "0.03 | \n", + "0.12 | \n", + "
14 | \n", + "lambdas5[ls_p3] | \n", + "0.99 | \n", + "lambdas5 | \n", + "0.98 | \n", + "2.61 | \n", + "0.62 | \n", + "1.61 | \n", + "21.47 | \n", + "0.05 | \n", + "0.12 | \n", + "
\n", + " | mean | \n", + "sd | \n", + "hdi_3% | \n", + "hdi_97% | \n", + "mcse_mean | \n", + "mcse_sd | \n", + "ess_bulk | \n", + "ess_tail | \n", + "r_hat | \n", + "
---|---|---|---|---|---|---|---|---|---|
lambdas1[se_acad_p1] | \n", + "1.000 | \n", + "0.000 | \n", + "1.000 | \n", + "1.000 | \n", + "0.000 | \n", + "0.000 | \n", + "40000.0 | \n", + "40000.0 | \n", + "NaN | \n", + "
lambdas1[se_acad_p2] | \n", + "0.825 | \n", + "0.055 | \n", + "0.725 | \n", + "0.930 | \n", + "0.001 | \n", + "0.000 | \n", + "9636.0 | \n", + "15616.0 | \n", + "1.0 | \n", + "
lambdas1[se_acad_p3] | \n", + "0.982 | \n", + "0.063 | \n", + "0.863 | \n", + "1.101 | \n", + "0.001 | \n", + "0.000 | \n", + "8860.0 | \n", + "14667.0 | \n", + "1.0 | \n", + "
lambdas2[se_social_p1] | \n", + "1.000 | \n", + "0.000 | \n", + "1.000 | \n", + "1.000 | \n", + "0.000 | \n", + "0.000 | \n", + "40000.0 | \n", + "40000.0 | \n", + "NaN | \n", + "
lambdas2[se_social_p2] | \n", + "0.999 | \n", + "0.062 | \n", + "0.885 | \n", + "1.118 | \n", + "0.001 | \n", + "0.001 | \n", + "5688.0 | \n", + "9867.0 | \n", + "1.0 | \n", + "
lambdas2[se_social_p3] | \n", + "0.952 | \n", + "0.075 | \n", + "0.816 | \n", + "1.098 | \n", + "0.001 | \n", + "0.001 | \n", + "9841.0 | \n", + "16162.0 | \n", + "1.0 | \n", + "
lambdas3[sup_friends_p1] | \n", + "1.000 | \n", + "0.000 | \n", + "1.000 | \n", + "1.000 | \n", + "0.000 | \n", + "0.000 | \n", + "40000.0 | \n", + "40000.0 | \n", + "NaN | \n", + "
lambdas3[sup_friends_p2] | \n", + "0.804 | \n", + "0.045 | \n", + "0.720 | \n", + "0.888 | \n", + "0.000 | \n", + "0.000 | \n", + "10940.0 | \n", + "18878.0 | \n", + "1.0 | \n", + "
lambdas3[sup_friends_p3] | \n", + "0.908 | \n", + "0.052 | \n", + "0.813 | \n", + "1.010 | \n", + "0.000 | \n", + "0.000 | \n", + "12075.0 | \n", + "20292.0 | \n", + "1.0 | \n", + "
lambdas4[sup_parents_p1] | \n", + "1.000 | \n", + "0.000 | \n", + "1.000 | \n", + "1.000 | \n", + "0.000 | \n", + "0.000 | \n", + "40000.0 | \n", + "40000.0 | \n", + "NaN | \n", + "
lambdas4[sup_parents_p2] | \n", + "1.013 | \n", + "0.054 | \n", + "0.915 | \n", + "1.117 | \n", + "0.001 | \n", + "0.000 | \n", + "8953.0 | \n", + "15516.0 | \n", + "1.0 | \n", + "
lambdas4[sup_parents_p3] | \n", + "0.979 | \n", + "0.059 | \n", + "0.869 | \n", + "1.093 | \n", + "0.001 | \n", + "0.000 | \n", + "12016.0 | \n", + "19450.0 | \n", + "1.0 | \n", + "
lambdas5[ls_p1] | \n", + "1.000 | \n", + "0.000 | \n", + "1.000 | \n", + "1.000 | \n", + "0.000 | \n", + "0.000 | \n", + "40000.0 | \n", + "40000.0 | \n", + "NaN | \n", + "
lambdas5[ls_p2] | \n", + "0.547 | \n", + "0.046 | \n", + "0.463 | \n", + "0.634 | \n", + "0.000 | \n", + "0.000 | \n", + "23600.0 | \n", + "28513.0 | \n", + "1.0 | \n", + "
lambdas5[ls_p3] | \n", + "0.656 | \n", + "0.056 | \n", + "0.552 | \n", + "0.759 | \n", + "0.000 | \n", + "0.000 | \n", + "21916.0 | \n", + "27988.0 | \n", + "1.0 | \n", + "
beta_r[SUP_F->SE_ACAD] | \n", + "0.049 | \n", + "0.040 | \n", + "-0.028 | \n", + "0.122 | \n", + "0.000 | \n", + "0.000 | \n", + "33619.0 | \n", + "30265.0 | \n", + "1.0 | \n", + "
beta_r[SUP_P->SE_ACAD] | \n", + "0.220 | \n", + "0.043 | \n", + "0.138 | \n", + "0.301 | \n", + "0.000 | \n", + "0.000 | \n", + "26087.0 | \n", + "27608.0 | \n", + "1.0 | \n", + "
beta_r[SUP_F->SE_SOC] | \n", + "0.146 | \n", + "0.035 | \n", + "0.080 | \n", + "0.213 | \n", + "0.000 | \n", + "0.000 | \n", + "26552.0 | \n", + "29710.0 | \n", + "1.0 | \n", + "
beta_r[SUP_P->SE_SOC] | \n", + "0.271 | \n", + "0.039 | \n", + "0.198 | \n", + "0.344 | \n", + "0.000 | \n", + "0.000 | \n", + "18597.0 | \n", + "25964.0 | \n", + "1.0 | \n", + "
beta_r2[SE_ACAD] | \n", + "0.166 | \n", + "0.074 | \n", + "0.028 | \n", + "0.305 | \n", + "0.000 | \n", + "0.000 | \n", + "41792.0 | \n", + "31794.0 | \n", + "1.0 | \n", + "
beta_r2[SE_SOCIAL] | \n", + "0.272 | \n", + "0.080 | \n", + "0.118 | \n", + "0.420 | \n", + "0.000 | \n", + "0.000 | \n", + "42014.0 | \n", + "31550.0 | \n", + "1.0 | \n", + "
beta_r2[SUP_F] | \n", + "0.063 | \n", + "0.057 | \n", + "-0.043 | \n", + "0.171 | \n", + "0.000 | \n", + "0.000 | \n", + "34544.0 | \n", + "27449.0 | \n", + "1.0 | \n", + "
beta_r2[SUP_P] | \n", + "0.251 | \n", + "0.062 | \n", + "0.136 | \n", + "0.369 | \n", + "0.000 | \n", + "0.000 | \n", + "29584.0 | \n", + "30999.0 | \n", + "1.0 | \n", + "
Psi[se_acad_p1] | \n", + "0.417 | \n", + "0.029 | \n", + "0.362 | \n", + "0.471 | \n", + "0.000 | \n", + "0.000 | \n", + "11409.0 | \n", + "16465.0 | \n", + "1.0 | \n", + "
Psi[se_acad_p2] | \n", + "0.413 | \n", + "0.024 | \n", + "0.366 | \n", + "0.457 | \n", + "0.000 | \n", + "0.000 | \n", + "19369.0 | \n", + "24906.0 | \n", + "1.0 | \n", + "
Psi[se_acad_p3] | \n", + "0.462 | \n", + "0.028 | \n", + "0.408 | \n", + "0.516 | \n", + "0.000 | \n", + "0.000 | \n", + "17531.0 | \n", + "22823.0 | \n", + "1.0 | \n", + "
Psi[se_social_p1] | \n", + "0.444 | \n", + "0.027 | \n", + "0.394 | \n", + "0.494 | \n", + "0.000 | \n", + "0.000 | \n", + "14886.0 | \n", + "22035.0 | \n", + "1.0 | \n", + "
Psi[se_social_p2] | \n", + "0.338 | \n", + "0.026 | \n", + "0.291 | \n", + "0.389 | \n", + "0.000 | \n", + "0.000 | \n", + "10327.0 | \n", + "17290.0 | \n", + "1.0 | \n", + "
Psi[se_social_p3] | \n", + "0.557 | \n", + "0.029 | \n", + "0.503 | \n", + "0.610 | \n", + "0.000 | \n", + "0.000 | \n", + "29639.0 | \n", + "29036.0 | \n", + "1.0 | \n", + "
Psi[sup_friends_p1] | \n", + "0.517 | \n", + "0.039 | \n", + "0.444 | \n", + "0.591 | \n", + "0.000 | \n", + "0.000 | \n", + "10615.0 | \n", + "15242.0 | \n", + "1.0 | \n", + "
Psi[sup_friends_p2] | \n", + "0.508 | \n", + "0.031 | \n", + "0.450 | \n", + "0.566 | \n", + "0.000 | \n", + "0.000 | \n", + "18625.0 | \n", + "24298.0 | \n", + "1.0 | \n", + "
Psi[sup_friends_p3] | \n", + "0.624 | \n", + "0.036 | \n", + "0.556 | \n", + "0.691 | \n", + "0.000 | \n", + "0.000 | \n", + "21581.0 | \n", + "25635.0 | \n", + "1.0 | \n", + "
Psi[sup_parents_p1] | \n", + "0.541 | \n", + "0.035 | \n", + "0.477 | \n", + "0.609 | \n", + "0.000 | \n", + "0.000 | \n", + "14766.0 | \n", + "22528.0 | \n", + "1.0 | \n", + "
Psi[sup_parents_p2] | \n", + "0.537 | \n", + "0.037 | \n", + "0.468 | \n", + "0.605 | \n", + "0.000 | \n", + "0.000 | \n", + "13008.0 | \n", + "18715.0 | \n", + "1.0 | \n", + "
Psi[sup_parents_p3] | \n", + "0.684 | \n", + "0.038 | \n", + "0.612 | \n", + "0.754 | \n", + "0.000 | \n", + "0.000 | \n", + "21999.0 | \n", + "26864.0 | \n", + "1.0 | \n", + "
Psi[ls_p1] | \n", + "0.537 | \n", + "0.051 | \n", + "0.442 | \n", + "0.633 | \n", + "0.001 | \n", + "0.000 | \n", + "6824.0 | \n", + "10978.0 | \n", + "1.0 | \n", + "
Psi[ls_p2] | \n", + "0.552 | \n", + "0.030 | \n", + "0.496 | \n", + "0.608 | \n", + "0.000 | \n", + "0.000 | \n", + "21921.0 | \n", + "25170.0 | \n", + "1.0 | \n", + "
Psi[ls_p3] | \n", + "0.670 | \n", + "0.036 | \n", + "0.603 | \n", + "0.740 | \n", + "0.000 | \n", + "0.000 | \n", + "19160.0 | \n", + "24500.0 | \n", + "1.0 | \n", + "
tau[se_acad_p1] | \n", + "5.058 | \n", + "0.048 | \n", + "4.966 | \n", + "5.148 | \n", + "0.001 | \n", + "0.001 | \n", + "4545.0 | \n", + "10287.0 | \n", + "1.0 | \n", + "
tau[se_acad_p2] | \n", + "5.266 | \n", + "0.042 | \n", + "5.186 | \n", + "5.345 | \n", + "0.001 | \n", + "0.000 | \n", + "5105.0 | \n", + "12105.0 | \n", + "1.0 | \n", + "
tau[se_acad_p3] | \n", + "5.115 | \n", + "0.049 | \n", + "5.022 | \n", + "5.208 | \n", + "0.001 | \n", + "0.000 | \n", + "4915.0 | \n", + "12071.0 | \n", + "1.0 | \n", + "
tau[se_social_p1] | \n", + "5.175 | \n", + "0.046 | \n", + "5.087 | \n", + "5.262 | \n", + "0.001 | \n", + "0.001 | \n", + "3954.0 | \n", + "9674.0 | \n", + "1.0 | \n", + "
tau[se_social_p2] | \n", + "5.364 | \n", + "0.043 | \n", + "5.283 | \n", + "5.444 | \n", + "0.001 | \n", + "0.001 | \n", + "3632.0 | \n", + "8857.0 | \n", + "1.0 | \n", + "
tau[se_social_p3] | \n", + "5.327 | \n", + "0.049 | \n", + "5.236 | \n", + "5.421 | \n", + "0.001 | \n", + "0.000 | \n", + "5021.0 | \n", + "11942.0 | \n", + "1.0 | \n", + "
tau[sup_friends_p1] | \n", + "5.607 | \n", + "0.070 | \n", + "5.473 | \n", + "5.735 | \n", + "0.001 | \n", + "0.001 | \n", + "3545.0 | \n", + "7220.0 | \n", + "1.0 | \n", + "
tau[sup_friends_p2] | \n", + "5.864 | \n", + "0.059 | \n", + "5.754 | \n", + "5.979 | \n", + "0.001 | \n", + "0.001 | \n", + "3903.0 | \n", + "8593.0 | \n", + "1.0 | \n", + "
tau[sup_friends_p3] | \n", + "5.822 | \n", + "0.068 | \n", + "5.696 | \n", + "5.954 | \n", + "0.001 | \n", + "0.001 | \n", + "4102.0 | \n", + "8858.0 | \n", + "1.0 | \n", + "
tau[sup_parents_p1] | \n", + "5.769 | \n", + "0.068 | \n", + "5.641 | \n", + "5.895 | \n", + "0.001 | \n", + "0.001 | \n", + "3000.0 | \n", + "7066.0 | \n", + "1.0 | \n", + "
tau[sup_parents_p2] | \n", + "5.719 | \n", + "0.068 | \n", + "5.587 | \n", + "5.843 | \n", + "0.001 | \n", + "0.001 | \n", + "3132.0 | \n", + "7931.0 | \n", + "1.0 | \n", + "
tau[sup_parents_p3] | \n", + "5.512 | \n", + "0.071 | \n", + "5.378 | \n", + "5.644 | \n", + "0.001 | \n", + "0.001 | \n", + "3647.0 | \n", + "9103.0 | \n", + "1.0 | \n", + "
tau[ls_p1] | \n", + "5.010 | \n", + "0.073 | \n", + "4.873 | \n", + "5.149 | \n", + "0.001 | \n", + "0.001 | \n", + "4056.0 | \n", + "9242.0 | \n", + "1.0 | \n", + "
tau[ls_p2] | \n", + "5.671 | \n", + "0.050 | \n", + "5.578 | \n", + "5.765 | \n", + "0.001 | \n", + "0.000 | \n", + "5777.0 | \n", + "13336.0 | \n", + "1.0 | \n", + "
tau[ls_p3] | \n", + "5.096 | \n", + "0.060 | \n", + "4.984 | \n", + "5.210 | \n", + "0.001 | \n", + "0.001 | \n", + "5766.0 | \n", + "12740.0 | \n", + "1.0 | \n", + "
\n", + " | SUP_P -> SE_SOC ->LS | \n", + "SUP_P -> SE_ACAD ->LS | \n", + "Total Indirect Effects SUP_P | \n", + "Total Effects SUP_P | \n", + "
---|---|---|---|---|
SEM0 | \n", + "0.073712 | \n", + "0.03652 | \n", + "0.110232 | \n", + "0.361232 | \n", + "
SEM1 | \n", + "0.133672 | \n", + "0.04914 | \n", + "0.182812 | \n", + "0.471812 | \n", + "
SEM2 | \n", + "0.177920 | \n", + "0.04840 | \n", + "0.226320 | \n", + "0.515320 | \n", + "
\n", + " | SUP_F -> SE_SOC ->LS | \n", + "SUP_F -> SE_ACAD ->LS | \n", + "Total Indirect Effects SUP_F | \n", + "Total Effects SUP_F | \n", + "
---|---|---|---|---|
SEM0 | \n", + "0.039712 | \n", + "0.008134 | \n", + "0.047846 | \n", + "0.110846 | \n", + "
SEM1 | \n", + "0.068572 | \n", + "0.009828 | \n", + "0.078400 | \n", + "0.127400 | \n", + "
SEM2 | \n", + "0.089516 | \n", + "0.009152 | \n", + "0.098668 | \n", + "0.130668 | \n", + "
\n", + " | rank | \n", + "elpd_loo | \n", + "p_loo | \n", + "elpd_diff | \n", + "weight | \n", + "se | \n", + "dse | \n", + "warning | \n", + "scale | \n", + "
---|---|---|---|---|---|---|---|---|---|
MM | \n", + "0 | \n", + "-3728.300062 | \n", + "994.604514 | \n", + "0.000000 | \n", + "8.023087e-01 | \n", + "65.332293 | \n", + "0.000000 | \n", + "True | \n", + "log | \n", + "
SEM0 | \n", + "1 | \n", + "-3778.256742 | \n", + "1109.385888 | \n", + "49.956680 | \n", + "1.976913e-01 | \n", + "64.764420 | \n", + "13.618924 | \n", + "True | \n", + "log | \n", + "
SEM1 | \n", + "2 | \n", + "-3781.419677 | \n", + "1104.681730 | \n", + "53.119615 | \n", + "3.276563e-15 | \n", + "64.853007 | \n", + "13.459803 | \n", + "True | \n", + "log | \n", + "
SEM2 | \n", + "3 | \n", + "-3782.787099 | \n", + "1102.006963 | \n", + "54.487037 | \n", + "0.000000e+00 | \n", + "64.871911 | \n", + "13.330740 | \n", + "True | \n", + "log | \n", + "