Equity is a fundamental value and guiding principle of education policy, but it is not necessarily actualised in education systems around the world. In order to investigate educational equity in the difference of academic performance between gender groups, females and males, we collect international education data from the Internet. PISA is an international assessment of 15-year-old students’ capabilities in reading literacy, mathematics literacy, and science literacy as well as measuring a wider range of factors including students’ interest, attitudes and motivation. It is distributed across over 60 countries, and student background questionnaires and teacher questionnaires are collected as part of PISA assessment. Student scores vary greatly for different student subpopulations within a jurisdiction – e.g., gender. In this project, we are specifically interested in describing and explaining gender differences in students’ performances scores across countries. We hope to identify countries that have “equitable” schooling outcomes and their characteristics in education systems, including student and school culture, teacher educational practices, and societal factors. That said, we caution against simplistic international comparisons of country performances using correlates of higher performance in higher ranking countries for projecting causal generalizations and statements.
To use PISA-WB analytic tool, public users such as parents, teachers and students should be able to have familiarity with operating graphical user interfaces (point, click, drop-down filters for interactive graphs).
International organizations such as World Bank, UNESCO, International Association for Evaluation of Educational Achievement (IEA), Educational Testing Service (ETS)
Test experts, teachers, researchers specified in educational measurement and policies, and enthusiastic parents who are data-driven decision makers are welcome to use our analysis tool. Users are expected to know the basic commands of computing, especially in Jupyter Notebook, and make right responses for commands and interpretation. They should have some encounter with Jupyter Notebook which is optimal to enable sharing of notebooks with other colleagues for more in-depth analysis. Benefit of using Jupyter is that users can see the code as well as the actual results of running the code. It is especially helpful for the users to see some text/instructions mixed with the code in a notebook.
Education researchers and measurement experts should have in-depth knowledge of interpreting and using modeling results from hierarchical linear modeling. They should master certain level of data analysis in python language and common statistic packages.
Datasets are downloadable from the following link: PISA international: http://www.oecd.org/pisa/data/2015database/ World Bank: http://datatopics.worldbank.org/education/indicators
- Student (STU): Student questionnaire data file in the most recent PISA 2015 dataset.
- School (SCH): School questionnaire data file in the most recent PISA 2015 dataset.
- Teacher (TEA): Teacher questionnaire data file in the most recent PISA 2015 dataset.
- Economic social cultural status (ESCS): Rescaled indices of economic, social and cultural status for countries for trend analysis. Available in PISA 2012 dataset.
- Country equity indicator (CEI): Education equity indicators at the country level from World Bank data sets including Multiple Indicator Cluster Survey and Urban Informal Settlement Survey in year 2015. Selected series are education equality indicators such as total net attendance rate, lower secondary, gender parity index (GPI). Three aspects of the design of PISA need careful attention in any analysis. The first stems from the sample design. Schools and students had unequal but known probabilities of selection. As a consequence, to generalize to the population sampled, analyses will need to apply the sampling weights provided in the file.
The second aspect to be considered also stems from the sampling design and bears on the calculation of standard errors. Since the sample design is a two-stage, stratified cluster design, we decide to do hierarchical linear modeling to account for the clusterness of the data.
Thirdly, PISA has special designs for student scores. PISA datasets include sets of five “plausible values” for each student for each overall subject area score and each subscale score. The plausible values are intended to represent the estimated distribution of scores of students similar to the given student in terms of responses to the assessment items and background questionnaire items. What this means for analyses is that, when it comes to statistics involving the achievement scores we use the approach of doing it five times, once for each plausible value, and then average the results.
A metadata of PISA student variable names is shown in the following:
import correlation as corrvisual
corrvisual.main()
import importlib
import hlm_pymer4 as hpm
importlib.reload(hpm)
hpm.main()/home/rohit000/anaconda3/lib/python3.7/site-packages/rpy2/robjects/pandas2ri.py:191: FutureWarning: from_items is deprecated. Please use DataFrame.from_dict(dict(items), ...) instead. DataFrame.from_dict(OrderedDict(items)) may be used to preserve the key order.
res = PandasDataFrame.from_items(items)
Formula: Science ~ female + (female*ESCS | CountryID)
Family: gaussian Inference: parametric
Number of observations: 186394 Groups: {'CountryID': 64.0}
Log-likelihood: -1077355.186 AIC: 2154736.372
Random effects:
Name Var Std
CountryID (Intercept) 7094.814 84.231
CountryID female 61.536 7.844
CountryID ESCS 1174.692 34.274
CountryID female:ESCS 0.355 0.596
Residual 6105.794 78.140
IV1 IV2 Corr
CountryID (Intercept) female -0.798
CountryID (Intercept) ESCS 0.883
CountryID (Intercept) female:ESCS 0.819
CountryID female ESCS -0.807
CountryID female female:ESCS -0.464
CountryID ESCS female:ESCS 0.738
Fixed effects:
Formula: Science ~ female + (female*ESCS | CountryID)
Family: gaussian Inference: parametric
Number of observations: 186394 Groups: {'CountryID': 64.0}
Log-likelihood: -1077355.186 AIC: 2154736.372
Random effects:
Name Var Std
CountryID (Intercept) 7094.814 84.231
CountryID female 61.536 7.844
CountryID ESCS 1174.692 34.274
CountryID female:ESCS 0.355 0.596
Residual 6105.794 78.140
IV1 IV2 Corr
CountryID (Intercept) female -0.798
CountryID (Intercept) ESCS 0.883
CountryID (Intercept) female:ESCS 0.819
CountryID female ESCS -0.807
CountryID female female:ESCS -0.464
CountryID ESCS female:ESCS 0.738
Fixed effects:
Estimate 2.5_ci 97.5_ci SE DF T-stat P-val Sig
(Intercept) 412.299 402.646 421.951 4.925 64.236 83.721 0.0 ***
female 6.220 5.031 7.410 0.607 64.815 10.247 0.0 ***
/home/rohit000/anaconda3/lib/python3.7/site-packages/scipy/stats/stats.py:1713: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.
return np.add.reduce(sorted[indexer] * weights, axis=axis) / sumval
Model failed to converge with max|grad| = 0.00297456 (tol = 0.002, component 1)
Formula: log_science ~ IBTEACH + WEALTH + ESCS + female + Sch_science_resource + (1 | SchoolID/CountryID)
Family: gaussian Inference: parametric
Number of observations: 186394 Groups: {'CountryID:SchoolID': 14419.0, 'SchoolID': 14419.0}
Log-likelihood: 79778.004 AIC: -159538.007
Random effects:
Name Var Std
CountryID:SchoolID (Intercept) 0.007 0.081
SchoolID (Intercept) 0.011 0.104
Residual 0.021 0.144
No random effect correlations specified
Fixed effects:
Formula: log_science ~ IBTEACH + WEALTH + ESCS + female + Sch_science_resource + (1 | SchoolID/CountryID)
Family: gaussian Inference: parametric
Number of observations: 186394 Groups: {'CountryID:SchoolID': 14419.0, 'SchoolID': 14419.0}
Log-likelihood: 79778.004 AIC: -159538.007
Random effects:
Name Var Std
CountryID:SchoolID (Intercept) 0.007 0.081
SchoolID (Intercept) 0.011 0.104
Residual 0.021 0.144
No random effect correlations specified
Fixed effects:
Estimate 2.5_ci 97.5_ci SE DF T-stat \
(Intercept) 6.075 6.069 6.080 0.003 14556.606 2254.813
IBTEACH -0.015 -0.016 -0.014 0.000 179429.792 -40.691
WEALTH -0.011 -0.012 -0.010 0.000 185101.967 -23.001
ESCS 0.042 0.041 0.043 0.000 183270.569 84.412
female -0.006 -0.007 -0.006 0.000 179221.977 -16.585
Sch_science_resource 0.016 0.015 0.017 0.001 14000.789 30.983
P-val Sig
(Intercept) 0.0 ***
IBTEACH 0.0 ***
WEALTH 0.0 ***
ESCS 0.0 ***
female 0.0 ***
Sch_science_resource 0.0 ***
Multiple random effects clusters specified in model. Plotting the 1 one. This can be changed by passing 'ranef_idx = number'
Formula: log_science ~ IBTEACH + WEALTH + ESCS + female + Sch_science_resource + female*ESCS + female*WEALTH + female*IBTEACH + (ESCS | CountryID)
Family: gaussian Inference: parametric
Number of observations: 186394 Groups: {'CountryID': 64.0}
Log-likelihood: 68151.331 AIC: -136276.662
Random effects:
Name Var Std
CountryID (Intercept) 0.009 0.094
CountryID ESCS 0.000 0.018
Residual 0.028 0.168
IV1 IV2 Corr
CountryID (Intercept) ESCS 0.228
Fixed effects:
Formula: log_science ~ IBTEACH + WEALTH + ESCS + female + Sch_science_resource + female*ESCS + female*WEALTH + female*IBTEACH + (ESCS | CountryID)
Family: gaussian Inference: parametric
Number of observations: 186394 Groups: {'CountryID': 64.0}
Log-likelihood: 68151.331 AIC: -136276.662
Random effects:
Name Var Std
CountryID (Intercept) 0.009 0.094
CountryID ESCS 0.000 0.018
Residual 0.028 0.168
IV1 IV2 Corr
CountryID (Intercept) ESCS 0.228
Fixed effects:
Estimate 2.5_ci 97.5_ci SE DF T-stat \
(Intercept) 6.108 6.085 6.131 0.012 64.904 518.956
IBTEACH -0.017 -0.017 -0.016 0.000 186330.747 -40.682
WEALTH -0.013 -0.014 -0.012 0.001 184730.141 -26.162
ESCS 0.075 0.070 0.079 0.002 65.958 32.646
female 0.001 -0.000 0.001 0.000 186282.256 1.614
Sch_science_resource 0.011 0.010 0.011 0.000 186364.965 51.874
ESCS:female -0.001 -0.002 0.000 0.000 186309.762 -1.622
WEALTH:female 0.002 0.001 0.003 0.000 186286.648 4.081
IBTEACH:female 0.004 0.003 0.005 0.000 186276.681 10.300
P-val Sig
(Intercept) 0.000 ***
IBTEACH 0.000 ***
WEALTH 0.000 ***
ESCS 0.000 ***
female 0.107
Sch_science_resource 0.000 ***
ESCS:female 0.105
WEALTH:female 0.000 ***
IBTEACH:female 0.000 ***
Besides running the main function, users can also call a specific function and are able to specify a particular variable to see the visualization.
import pandas as pd
import hlm_pymer4 as hpm
df = pd.read_csv('data/sample data.csv').groupby(['CountryID', 'SchoolID']).apply(
lambda x: x.sample(frac=0.02, random_state=999)).reset_index(drop=True)
model_5_sci = hpm.mixeff_multinteraction2level_model(df)
model_sum_visual(model_5_sci, 'WEALTH', 'log_science')/home/rohit000/anaconda3/lib/python3.7/site-packages/rpy2/rinterface/__init__.py:146: RRuntimeWarning: singular fit
warnings.warn(x, RRuntimeWarning)
/home/rohit000/anaconda3/lib/python3.7/site-packages/rpy2/robjects/pandas2ri.py:191: FutureWarning: from_items is deprecated. Please use DataFrame.from_dict(dict(items), ...) instead. DataFrame.from_dict(OrderedDict(items)) may be used to preserve the key order.
res = PandasDataFrame.from_items(items)
singular fit
Formula: log_science ~ IBTEACH + WEALTH + ESCS + female + Sch_science_resource + female*ESCS + female*WEALTH + female*IBTEACH + (ESCS | CountryID)
Family: gaussian Inference: parametric
Number of observations: 273 Groups: {'CountryID': 10.0}
Log-likelihood: 57.322 AIC: -88.644
Random effects:
Name Var Std
CountryID (Intercept) 0.014 0.119
CountryID ESCS 0.000 0.006
Residual 0.036 0.189
IV1 IV2 Corr
CountryID (Intercept) ESCS -1.0
Fixed effects:
Formula: log_science ~ IBTEACH + WEALTH + ESCS + female + Sch_science_resource + female*ESCS + female*WEALTH + female*IBTEACH + (ESCS | CountryID)
Family: gaussian Inference: parametric
Number of observations: 273 Groups: {'CountryID': 10.0}
Log-likelihood: 57.322 AIC: -88.644
Random effects:
Name Var Std
CountryID (Intercept) 0.014 0.119
CountryID ESCS 0.000 0.006
Residual 0.036 0.189
IV1 IV2 Corr
CountryID (Intercept) ESCS -1.0
Fixed effects:
Estimate 2.5_ci 97.5_ci SE DF T-stat \
(Intercept) 6.023 5.909 6.136 0.058 17.221 104.403
IBTEACH -0.010 -0.032 0.011 0.011 260.731 -0.945
WEALTH -0.051 -0.076 -0.027 0.013 266.076 -4.080
ESCS 0.089 0.058 0.120 0.016 66.163 5.592
female -0.002 -0.026 0.022 0.012 265.094 -0.189
Sch_science_resource 0.016 0.002 0.030 0.007 240.981 2.263
ESCS:female 0.019 -0.011 0.048 0.015 258.607 1.229
WEALTH:female -0.009 -0.032 0.013 0.012 261.400 -0.821
IBTEACH:female 0.004 -0.018 0.025 0.011 261.497 0.343
P-val Sig
(Intercept) 0.000 ***
IBTEACH 0.345
WEALTH 0.000 ***
ESCS 0.000 ***
female 0.850
Sch_science_resource 0.024 *
ESCS:female 0.220
WEALTH:female 0.412
IBTEACH:female 0.732
/home/rohit000/anaconda3/lib/python3.7/site-packages/scipy/stats/stats.py:1713: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.
return np.add.reduce(sorted[indexer] * weights, axis=axis) / sumval
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
<ipython-input-52-b751b572170d> in <module>()
4 lambda x: x.sample(frac=0.02, random_state=999)).reset_index(drop=True)
5 model_5_sci = hpm.mixeff_multinteraction2level_model(df)
----> 6 model_sum_visual(model_5_sci, 'WEALTH', 'log_science')
TypeError: model_sum_visual() takes 2 positional arguments but 3 were given
Now, let's look at how users can interact with our formula generator andn fun customized models on their own:
We will first import data. For illustration, here we sub-sample a small dataset.
import pandas as pd
import seaborn as sns
from pymer4.models import Lmer
df = pd.read_csv('data/sample data.csv').groupby(['CountryID', 'SchoolID']).apply(
lambda x: x.sample(frac=0.02, random_state=999)).reset_index(drop=True)
df.head()
<style scoped>
.dataframe tbody tr th:only-of-type {
vertical-align: middle;
}
</style>
.dataframe tbody tr th {
vertical-align: top;
}
.dataframe thead th {
text-align: right;
}
| Unnamed: 0 | Unnamed: 0.1 | Unnamed: 0.1.1 | CountryID | SchoolID | StudentID | Gender | CountryName | CountryCode | Continent | ... | Science | IBTEACH | WEALTH | ESCS | School_type | Sch_science_resource | log_science | female | z_sch_resource | z_IBTEACH | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 12461 | 34745 | 34745 | 56 | 5650027 | 5651417 | Male | Belgium - Rest of the country | BEL | EU | ... | 586.4260 | -1.0435 | -0.0739 | 1.0494 | -1.0 | 5.0 | 6.374046 | -1 | 0.119012 | -1.099643 |
| 1 | 13154 | 36507 | 36507 | 56 | 5650078 | 5652526 | Female | Belgium - Rest of the country | BEL | EU | ... | 684.0211 | -0.1798 | -0.6315 | -0.2282 | -1.0 | 6.0 | 6.527989 | 1 | 0.569286 | -0.246594 |
| 2 | 59526 | 196764 | 196764 | 352 | 35200004 | 35203363 | Male | Iceland | ISL | EU | ... | 474.4032 | -0.0748 | -0.5411 | 1.1494 | 1.0 | 4.0 | 6.162058 | -1 | -0.331262 | -0.142889 |
| 3 | 59801 | 197384 | 197384 | 352 | 35200034 | 35202216 | Female | Iceland | ISL | EU | ... | 593.7425 | 0.2049 | 0.2106 | 1.6585 | 1.0 | 5.0 | 6.386446 | 1 | 0.119012 | 0.133362 |
| 4 | 59898 | 197619 | 197619 | 352 | 35200042 | 35203996 | Male | Iceland | ISL | EU | ... | 448.1137 | 0.6256 | 0.3800 | 1.1325 | 1.0 | 5.0 | 6.105047 | -1 | 0.119012 | 0.548873 |
5 rows × 22 columns
Then, we will create multi-level formula by importing formula_creator tool. Here's an example of selecting students' reading scores this time as an outcome variable, and specify interactions, fixed, and random effects.
import formula_creator as mod
mod.main()Input outcome value:Reading
Input level values one by one, "s" to stop:
SchoolID
CountryID
s
Interaction? (y/n)y
Input interaction:
Input first var:WEALTH
Input second var:female
Stop inputing? (y/n)y
Fixed effect? (y/n)WEALTH
Random effect? (y/n)female
Want to input grand mean intercept? (y/n)n
Lmer('Reading ~ WEALTH*female + (1|SchoolID/CountryID)')
Random effect, 2-level, interation model
Now, we have created the formula as below. The users will need to copy-paste the formula and specify data in their own model. They would need to add .fit(REML=False) for the model to give estimation.
trial = Lmer('Reading ~ WEALTH*female + (1|SchoolID/CountryID)', data = df)
trial.fit(REML=False)/home/rohit000/anaconda3/lib/python3.7/site-packages/rpy2/robjects/pandas2ri.py:191: FutureWarning: from_items is deprecated. Please use DataFrame.from_dict(dict(items), ...) instead. DataFrame.from_dict(OrderedDict(items)) may be used to preserve the key order.
res = PandasDataFrame.from_items(items)
Formula: Reading ~ WEALTH*female + (1|SchoolID/CountryID)
Family: gaussian Inference: parametric
Number of observations: 273 Groups: {'CountryID:SchoolID': 224.0, 'SchoolID': 224.0}
Log-likelihood: -1637.889 AIC: 3289.778
Random effects:
Name Var Std
CountryID:SchoolID (Intercept) 2523.959 50.239
SchoolID (Intercept) 1223.756 34.982
Residual 6060.556 77.850
No random effect correlations specified
Fixed effects:
<style scoped>
.dataframe tbody tr th:only-of-type {
vertical-align: middle;
}
</style>
.dataframe tbody tr th {
vertical-align: top;
}
.dataframe thead th {
text-align: right;
}
| Estimate | 2.5_ci | 97.5_ci | SE | DF | T-stat | P-val | Sig | |
|---|---|---|---|---|---|---|---|---|
| (Intercept) | 458.577 | 445.969 | 471.184 | 6.433 | 213.850 | 71.290 | 0.000 | *** |
| WEALTH | -8.492 | -17.452 | 0.469 | 4.572 | 271.639 | -1.857 | 0.064 | . |
| female | 11.073 | -0.656 | 22.801 | 5.984 | 264.300 | 1.850 | 0.065 | . |
| WEALTH:female | -3.691 | -12.586 | 5.204 | 4.538 | 267.432 | -0.813 | 0.417 |
trial.coefs
<style scoped>
.dataframe tbody tr th:only-of-type {
vertical-align: middle;
}
</style>
.dataframe tbody tr th {
vertical-align: top;
}
.dataframe thead th {
text-align: right;
}
| Estimate | 2.5_ci | 97.5_ci | SE | DF | T-stat | P-val | Sig | |
|---|---|---|---|---|---|---|---|---|
| (Intercept) | 458.576618 | 445.969024 | 471.184212 | 6.432564 | 213.849570 | 71.289865 | 5.109954e-151 | *** |
| WEALTH | -8.491573 | -17.451781 | 0.468635 | 4.571619 | 271.638877 | -1.857454 | 6.432868e-02 | . |
| female | 11.072804 | -0.655574 | 22.801181 | 5.983976 | 264.300271 | 1.850409 | 6.537051e-02 | . |
| WEALTH:female | -3.690702 | -12.585737 | 5.204334 | 4.538367 | 267.431874 | -0.813222 | 4.168139e-01 |
trial.ranef_var
<style scoped>
.dataframe tbody tr th:only-of-type {
vertical-align: middle;
}
</style>
.dataframe tbody tr th {
vertical-align: top;
}
.dataframe thead th {
text-align: right;
}
| Name | Var | Std | |
|---|---|---|---|
| CountryID:SchoolID | (Intercept) | 2523.958941 | 50.239018 |
| SchoolID | (Intercept) | 1223.755513 | 34.982217 |
| Residual | 6060.556264 | 77.849575 |
trial.fixef[ (Intercept) WEALTH female WEALTH:female
0 490.833792 -8.491573 11.072804 -3.690702
1 504.427429 -8.491573 11.072804 -3.690702
2 453.878945 -8.491573 11.072804 -3.690702
3 507.802614 -8.491573 11.072804 -3.690702
4 476.191146 -8.491573 11.072804 -3.690702
5 438.527215 -8.491573 11.072804 -3.690702
6 478.729786 -8.491573 11.072804 -3.690702
7 483.912414 -8.491573 11.072804 -3.690702
8 407.875018 -8.491573 11.072804 -3.690702
9 454.968589 -8.491573 11.072804 -3.690702
10 496.226753 -8.491573 11.072804 -3.690702
11 486.119793 -8.491573 11.072804 -3.690702
12 430.715097 -8.491573 11.072804 -3.690702
13 490.924392 -8.491573 11.072804 -3.690702
14 448.898633 -8.491573 11.072804 -3.690702
15 475.956719 -8.491573 11.072804 -3.690702
16 476.100709 -8.491573 11.072804 -3.690702
17 451.427922 -8.491573 11.072804 -3.690702
18 500.799305 -8.491573 11.072804 -3.690702
19 481.585169 -8.491573 11.072804 -3.690702
20 499.023817 -8.491573 11.072804 -3.690702
21 423.504879 -8.491573 11.072804 -3.690702
22 458.988330 -8.491573 11.072804 -3.690702
23 458.204129 -8.491573 11.072804 -3.690702
24 475.875129 -8.491573 11.072804 -3.690702
25 453.653911 -8.491573 11.072804 -3.690702
26 458.704693 -8.491573 11.072804 -3.690702
27 461.820289 -8.491573 11.072804 -3.690702
28 477.929499 -8.491573 11.072804 -3.690702
29 426.329597 -8.491573 11.072804 -3.690702
.. ... ... ... ...
194 432.898132 -8.491573 11.072804 -3.690702
195 458.806888 -8.491573 11.072804 -3.690702
196 417.017245 -8.491573 11.072804 -3.690702
197 484.361002 -8.491573 11.072804 -3.690702
198 474.822970 -8.491573 11.072804 -3.690702
199 440.298457 -8.491573 11.072804 -3.690702
200 422.049947 -8.491573 11.072804 -3.690702
201 469.571393 -8.491573 11.072804 -3.690702
202 428.569503 -8.491573 11.072804 -3.690702
203 456.664276 -8.491573 11.072804 -3.690702
204 449.273637 -8.491573 11.072804 -3.690702
205 474.357426 -8.491573 11.072804 -3.690702
206 434.105855 -8.491573 11.072804 -3.690702
207 420.419457 -8.491573 11.072804 -3.690702
208 445.405772 -8.491573 11.072804 -3.690702
209 445.695496 -8.491573 11.072804 -3.690702
210 458.325264 -8.491573 11.072804 -3.690702
211 463.326272 -8.491573 11.072804 -3.690702
212 482.370212 -8.491573 11.072804 -3.690702
213 415.134949 -8.491573 11.072804 -3.690702
214 470.105751 -8.491573 11.072804 -3.690702
215 465.665379 -8.491573 11.072804 -3.690702
216 452.230524 -8.491573 11.072804 -3.690702
217 423.767273 -8.491573 11.072804 -3.690702
218 413.162694 -8.491573 11.072804 -3.690702
219 428.195011 -8.491573 11.072804 -3.690702
220 391.875945 -8.491573 11.072804 -3.690702
221 400.313538 -8.491573 11.072804 -3.690702
222 421.620063 -8.491573 11.072804 -3.690702
223 466.652819 -8.491573 11.072804 -3.690702
[224 rows x 4 columns], (Intercept) WEALTH female WEALTH:female
0 474.216688 -8.491573 11.072804 -3.690702
1 480.807638 -8.491573 11.072804 -3.690702
2 456.298925 -8.491573 11.072804 -3.690702
3 482.444116 -8.491573 11.072804 -3.690702
4 467.117120 -8.491573 11.072804 -3.690702
5 448.855554 -8.491573 11.072804 -3.690702
6 468.347994 -8.491573 11.072804 -3.690702
7 470.860820 -8.491573 11.072804 -3.690702
8 433.993666 -8.491573 11.072804 -3.690702
9 456.827245 -8.491573 11.072804 -3.690702
10 476.831495 -8.491573 11.072804 -3.690702
11 471.931079 -8.491573 11.072804 -3.690702
12 445.067805 -8.491573 11.072804 -3.690702
13 474.260616 -8.491573 11.072804 -3.690702
14 453.884193 -8.491573 11.072804 -3.690702
15 467.003457 -8.491573 11.072804 -3.690702
16 467.073271 -8.491573 11.072804 -3.690702
17 455.110533 -8.491573 11.072804 -3.690702
18 479.048522 -8.491573 11.072804 -3.690702
19 469.732442 -8.491573 11.072804 -3.690702
20 478.187667 -8.491573 11.072804 -3.690702
21 441.571891 -8.491573 11.072804 -3.690702
22 458.776239 -8.491573 11.072804 -3.690702
23 458.396015 -8.491573 11.072804 -3.690702
24 466.963897 -8.491573 11.072804 -3.690702
25 456.189816 -8.491573 11.072804 -3.690702
26 458.638716 -8.491573 11.072804 -3.690702
27 460.149330 -8.491573 11.072804 -3.690702
28 467.959970 -8.491573 11.072804 -3.690702
29 442.941471 -8.491573 11.072804 -3.690702
.. ... ... ... ...
194 446.126261 -8.491573 11.072804 -3.690702
195 458.688266 -8.491573 11.072804 -3.690702
196 438.426325 -8.491573 11.072804 -3.690702
197 471.078320 -8.491573 11.072804 -3.690702
198 466.453752 -8.491573 11.072804 -3.690702
199 449.714350 -8.491573 11.072804 -3.690702
200 440.866459 -8.491573 11.072804 -3.690702
201 463.907496 -8.491573 11.072804 -3.690702
202 444.027502 -8.491573 11.072804 -3.690702
203 457.649408 -8.491573 11.072804 -3.690702
204 454.066016 -8.491573 11.072804 -3.690702
205 466.228031 -8.491573 11.072804 -3.690702
206 446.711832 -8.491573 11.072804 -3.690702
207 440.075907 -8.491573 11.072804 -3.690702
208 452.190660 -8.491573 11.072804 -3.690702
209 452.331135 -8.491573 11.072804 -3.690702
210 458.454747 -8.491573 11.072804 -3.690702
211 460.879514 -8.491573 11.072804 -3.690702
212 470.113074 -8.491573 11.072804 -3.690702
213 437.513683 -8.491573 11.072804 -3.690702
214 464.166582 -8.491573 11.072804 -3.690702
215 462.013643 -8.491573 11.072804 -3.690702
216 455.499679 -8.491573 11.072804 -3.690702
217 441.699114 -8.491573 11.072804 -3.690702
218 436.557425 -8.491573 11.072804 -3.690702
219 443.845927 -8.491573 11.072804 -3.690702
220 426.236426 -8.491573 11.072804 -3.690702
221 430.327440 -8.491573 11.072804 -3.690702
222 440.658027 -8.491573 11.072804 -3.690702
223 462.492409 -8.491573 11.072804 -3.690702
[224 rows x 4 columns]]
trial.plot_summary()Multiple random effects clusters specified in model. Plotting the 1 one. This can be changed by passing 'ranef_idx = number'
<matplotlib.axes._subplots.AxesSubplot at 0x7fa334016e80>
