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quantile_regression.py
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import statsmodels.formula.api as smf
import dash_bootstrap_components as dbc
from dash import dcc, html, dash_table
import dash
from plotly import graph_objects as go
import pandas as pd
import numpy as np
import json
import app_fxns
def generate_figure_quantile_regression():
return html.Div(
children=[
dcc.Loading(
type="default",
fullscreen=False,
children=html.Div(
children=[dcc.Graph(id="figure_quantile_regression"),
],
),
),
html.Br(),
html.P("Coefficients of determination (R\u00B2) for quantile regression " +
"are Cox-Snell likelihood ratio pseudo R\u00B2 values. They are not " +
"directly comparable to the r\u00B2 of ordinary least-squares " +
"regression.",
),
],
style={'width': '100%',
'display': 'inline-block',
'background-color': '#f0f0f0',
'padding': '1%',
},
)
def control_card_quantile_regression():
return html.Div(
id="control-card_quantile_regression",
children=[
html.H5("Conduct linear and polynomial quantile regression",
style={'display': 'inline-block',
'margin-right': '1%',
},
),
html.I(className="fas fa-question-circle fa-lg",
id="target_select_vars2_quant",
style={'display': 'inline-block',
'width': '3%',
'color':'#99ccff',
},
),
dbc.Tooltip("Data too noisy or too oddly distributed for ordinary least squares " +
"regression? Quantile regression makes no assumptions about the " +
"distribution of data and allows you to explore boundaries on the " +
"relationships between features.",
target="target_select_vars2_quant",
style = {'font-size': 12,
},
),
html.Hr(),
html.Div(
id="control-card2a_quant",
children=[
html.B("Choose a predictor (x) variable",
style={'display': 'inline-block',
'vertical-align': 'top',
},
),
dcc.Dropdown(
id='xvar2_quant',
options=[{"label": i, "value": i} for i in []],
multi=False,
optionHeight=65,
placeholder='Select a feature',
style={'width': '100%',
'display': 'inline-block',
},
),
],
style={'display': 'inline-block',
'vertical-align': 'top',
'margin-right': '1%',
'width': '20%',
}),
html.Div(
id="control-card2b_quant",
children=[
html.B("Choose a data transformation",
style={'display': 'inline-block',
'vertical-align': 'top',
}),
dcc.Dropdown(
id='x_transform_quant',
options=[{"label": i, "value": i} for i in ['None', 'log10',
'square root', 'cube root',
'squared', 'cubed',
'log-modulo', 'log-shift',
]
],
multi=False,
value='None',
style={'width': '90%',
'display': 'inline-block',
},
),
],
style={'display': 'inline-block',
'vertical-align': 'top',
'margin-right': '2%',
'width': '20%',
}),
html.Div(
id="control-card2c_quant",
children=[
html.B("Choose a response (y) variable",
style={'display': 'inline-block',
'vertical-align': 'top',
},
),
dcc.Dropdown(
id='yvar2_quant',
options=[{"label": i, "value": i} for i in []],
multi=False,
optionHeight=65,
placeholder='Select a feature',
style={'width': '100%',
'display': 'inline-block',
},
),
],
style={'display': 'inline-block',
'vertical-align': 'top',
'margin-right': '1%',
'width': '20%',
}),
html.Div(
id="control-card2d_quant",
children=[
html.B("Choose a data transformation",
style={'display': 'inline-block',
'vertical-align': 'top',
}),
dcc.Dropdown(
id='y_transform_quant',
options=[{"label": i, "value": i} for i in ['None', 'log10',
'square root', 'cube root',
'squared', 'cubed',
'log-modulo', 'log-shift',
]
],
multi=False,
value='None',
style={'width': '90%',
'display': 'inline-block',
},
),
],
style={'display': 'inline-block',
'vertical-align': 'top',
'margin-right': '2%',
'width': '20%',
},
),
html.Hr(),
html.Div(
id="control-card2e_quant_quantiles",
children=[
html.B("Choose lower and upper quantiles",
style={'display': 'inline-block',
'vertical-align': 'top',
},
),
dcc.RangeSlider(
id='quantiles',
min=1,
max=99,
value=[5, 95],
allowCross=False,
tooltip={"placement": "bottom",
"always_visible": True},
),
],
style={'display': 'inline-block',
'vertical-align': 'top',
'margin-right': '1%',
'width': '20%',
},
),
html.Div(
id="control-card2e_quant",
children=[
html.B("Choose a model",
style={'display': 'inline-block',
'vertical-align': 'top',
},
),
dcc.Dropdown(
id='model2_quant',
options=[{"label": i, "value": i} for i in ['linear',
'quadratic',
'cubic',
]
],
multi=False,
value='linear',
style={'width': '90%',
'display': 'inline-block',
},
),
],
style={'display': 'inline-block',
'vertical-align': 'top',
'margin-right': '2%',
'width': '20%',
},
),
dbc.Button('Run regression',
id='btn2_quant',
n_clicks=0,
style={'width': '20%',
'font-size': 12,
"background-color": "#2a8cff",
'display': 'inline-block',
'margin-right': '1%',
'margin-top': '1.7%',
},
),
dbc.Button("View results table",
id="open-quant_regression_table",
style={
"background-color": "#2a8cff",
'width': '16%',
'font-size': 12,
'display': 'inline-block',
'margin-top': '1.7%',
},
),
dbc.Modal(
[dbc.ModalBody([html.H5("Results for upper quantile:"),
html.Div(id="quant_table_1"),
html.Div(id="quant_table_2"),
html.Br(),
html.H5("Results for 50th quantile (aka Least Absolute " +
"Deviation Model):"),
html.Div(id="quant_table_3"),
html.Div(id="quant_table_4"),
html.Br(),
html.H5("Results for lower quantile:"),
html.Div(id="quant_table_5"),
html.Div(id="quant_table_6"),
html.Br(),
html.P("", id="quant_table_txt"),
]),
dbc.ModalFooter(
dbc.Button("Click to Close",
id="close-quant_regression_table",
className="ml-auto",
style={
"background-color": "#2a8cff",
'width': '30%',
'font-size': 14,
},
),
style={
"background-color": "#A0A0A0",
"display": "flex",
"justify-content": "center",
"align-items": "center",
},
),
],
id="modal-quant_regression_table",
is_open=False,
centered=True,
autoFocus=True,
size="lg",
keyboard=True,
fade=True,
backdrop=True,
),
html.P("", id='rt3_quant')
],
style={'width': '98.5%',
'margin-left': '1%',
},
)
def get_updated_results(n_clicks, xvar, yvar, x_transform, y_transform, model, df, quantiles):
cols = ['Model information', 'Model statistics']
df_table1 = pd.DataFrame(columns=cols)
df_table1['Model information'] = [np.nan]*3
df_table1['Model statistics'] = [np.nan]*3
dashT1 = dash_table.DataTable(
data=df_table1.to_dict('records'),
columns=[{'id': c, 'name': c} for c in df_table1.columns],
page_action='none',
sort_action="native",
sort_mode="multi",
filter_action="native",
style_table={'height': '300px',
'overflowY': 'auto',
},
style_cell={'padding':'5px',
'minwidth':'140px',
'width':'160px',
'maxwidth':'160px',
'whiteSpace':'normal',
'textAlign': 'center',
},
)
cols = ['Parameter', 'coef', 'std err', 't', 'P>|t|', '[0.025]', '[0.975]']
df_table2 = pd.DataFrame(columns=cols)
df_table2['Parameter'] = [np.nan]*3
df_table2['coef'] = [np.nan]*3
df_table2['std err'] = [np.nan]*3
df_table2['t'] = [np.nan]*3
df_table2['P>|t|'] = [np.nan]*3
df_table2['[0.025]'] = [np.nan]*3
dashT2 = dash_table.DataTable(
data=df_table2.to_dict('records'),
columns=[{'id': c, 'name': c} for c in df_table2.columns],
page_action='none',
sort_action="native",
sort_mode="multi",
filter_action="native",
style_table={'height': '300px',
'overflowY': 'auto',
},
style_cell={'padding':'5px',
'minwidth':'140px',
'width':'160px',
'maxwidth':'160px',
'whiteSpace':'normal',
'textAlign': 'center',
},
)
ctx1 = dash.callback_context
jd1 = json.dumps({'triggered': ctx1.triggered,})
jd1 = jd1[:50]
if 'rt4.children' in jd1:
return {}, "", "", dashT1, dashT2, dashT1, dashT2, dashT1, dashT2
if df is None or xvar is None or yvar is None or xvar == yvar or isinstance(yvar, list) is True or isinstance(yvar, list) is True:
if df is None:
return [{}, "", "", dashT1, dashT2, dashT1, dashT2, dashT1, dashT2]
elif (isinstance(xvar, list) is True or xvar is None) & (isinstance(yvar, list) is True or yvar is None):
return [{}, "Error: You need to select some variables.", "",
dashT1, dashT2, dashT1, dashT2, dashT1, dashT2]
elif isinstance(yvar, list) is True or yvar is None:
return [{}, "Error: You need to select a response variable.", "",
dashT1, dashT2, dashT1, dashT2, dashT1, dashT2]
elif isinstance(xvar, list) is True or xvar is None:
return [{}, "Error: You need to select an predictor variable.", "",
dashT1, dashT2, dashT1, dashT2, dashT1, dashT2]
elif xvar == yvar and xvar is not None:
return [{}, "Error: Your predictor variable and response variable are the same. Ensure they are different.",
"", dashT1, dashT2, dashT1, dashT2, dashT1, dashT2]
else:
return [{}, "", "", dashT1, dashT2, dashT1, dashT2, dashT1, dashT2]
else:
df = pd.DataFrame(df)
if df.empty:
return {}, "", "", dashT1, dashT2, dashT1, dashT2, dashT1, dashT2
df = df.filter(items=[xvar, yvar], axis=1)
if x_transform == 'log10':
df[xvar] = np.log10(df[xvar])
df.rename(columns={xvar: "log<sub>10</sub>(" + xvar + ")"}, inplace=True)
xvar = "log<sub>10</sub>(" + xvar + ")"
elif x_transform == 'square root':
df[xvar] = df[xvar]**0.5
df.rename(columns={xvar: "\u221A(" + xvar + ")"}, inplace=True)
xvar = "\u221A(" + xvar + ")"
elif x_transform == 'cube root':
df[xvar] = df[xvar]**(1/3)
df.rename(columns={xvar: "\u221B(" + xvar + ")"}, inplace=True)
xvar = "\u221B(" + xvar + ")"
elif x_transform == 'squared':
df[xvar] = df[xvar]**2
df.rename(columns={xvar: "(" + xvar + ")\u00B2"}, inplace=True)
xvar = "(" + xvar + ")\u00B2"
elif x_transform == 'cubed':
df.rename(columns={xvar: "(" + xvar + ")\u00B3"}, inplace=True)
xvar = "(" + xvar + ")\u00B3"
elif x_transform == 'log-modulo':
lmt = np.log10(np.abs(df[xvar]) + 1).tolist()
for i, val in enumerate(df[xvar].tolist()):
if val < 0:
lmt[i] = lmt[i] * -1
df[xvar] = lmt
df.rename(columns={xvar: "log-modulo(" + xvar + ")"}, inplace=True)
xvar = "log-modulo(" + xvar + ")"
elif x_transform == 'log-shift':
df[xvar] = np.log10(np.abs(df[xvar]) + 1).tolist()
df.rename(columns={xvar: "log-shift(" + xvar + ")"}, inplace=True)
xvar = "log-shift(" + xvar + ")"
if y_transform == 'log10':
df[yvar] = np.log10(df[yvar])
df.rename(columns={yvar: "log<sub>10</sub>(" + yvar + ")"}, inplace=True)
yvar = "log<sub>10</sub>(" + yvar + ")"
elif y_transform == 'square root':
df[yvar] = df[yvar]**0.5
df.rename(columns={yvar: "\u221A(" + yvar + ")"}, inplace=True)
yvar = "\u221A(" + yvar + ")"
elif y_transform == 'cube root':
df[yvar] = df[yvar]**(1/3)
df.rename(columns={yvar: "\u221B(" + yvar + ")"}, inplace=True)
yvar = "\u221B(" + yvar + ")"
elif y_transform == 'squared':
df[yvar] = df[yvar]**2
df.rename(columns={yvar: "(" + yvar + ")\u00B2"}, inplace=True)
yvar = "(" + yvar + ")\u00B2"
elif y_transform == 'cubed':
df.rename(columns={yvar: "(" + yvar + ")\u00B3"}, inplace=True)
yvar = "(" + yvar + ")\u00B3"
elif y_transform == 'log-modulo':
lmt = np.log10(np.abs(df[yvar]) + 1).tolist()
for i, val in enumerate(df[yvar].tolist()):
if val < 0:
lmt[i] = lmt[i] * -1
df[yvar] = lmt
df.rename(columns={yvar: "log-modulo(" + yvar + ")"}, inplace=True)
yvar = "log-modulo(" + yvar + ")"
elif y_transform == 'log-shift':
df[yvar] = np.log10(df[yvar] + 1).tolist()
df.rename(columns={yvar: "log-shift(" + yvar + ")"}, inplace=True)
yvar = "log-shift(" + yvar + ")"
df.replace([np.inf, -np.inf], np.nan, inplace=True)
df.dropna(how='any', axis=0, inplace=True)
ql = quantiles[0]
qh = quantiles[1]
quantiles = [0.01*ql, 0.5, 0.01*qh]
formula = int()
#degree = int()
if model == 'linear':
formula = 'y ~ 1 + x'
#degree = 1
elif model == 'quadratic':
#degree = 2
formula = 'y ~ 1 + x + I(x ** 2.0)'
elif model == 'cubic':
#degree = 3
formula = 'y ~ 1 + x + I(x ** 3.0) + I(x ** 2.0)'
#########################################################################################
################## GET QUANTILE PREDICTIONS FOR EACH PLOT ###############################
#########################################################################################
# Polynomial Quantile regression
# Least Absolute Deviation (LAD)
# The LAD model is a special case of quantile regression where q=0.5
# #res = mod.fit(q=.5)
x, y = (np.array(t) for t in zip(*sorted(zip(df[xvar], df[yvar]))))
d = {'x': x, 'y': y}
df = pd.DataFrame(data=d)
mod = smf.quantreg(formula, df)
res_all = [mod.fit(q=q) for q in quantiles]
#res_ols = smf.ols(formula, df).fit()
x_p = np.array(x)
#df_p = pd.DataFrame({'x': x_p})
y_lo = res_all[0].fittedvalues
#y_lo_resid = res_all[0].resid
#obs_lo = y_lo - y_lo_resid
pr2_lo = str(np.round(res_all[0].prsquared, 3))
y_50 = res_all[1].fittedvalues
y_50_resid = res_all[1].resid
obs_50 = y_50 - y_50_resid
pr2_50 = str(np.round(res_all[1].prsquared, 3))
r2_50 = str(np.round(app_fxns.obs_pred_rsquare(obs_50, y_50), 3))
y_hi = res_all[2].fittedvalues
#y_hi_resid = res_all[2].resid
#obs_hi = y_hi - y_hi_resid
pr2_hi = str(np.round(res_all[2].prsquared, 3))
#y_ols_predicted = res_ols.predict(df_p)
del df
fig_data = []
clr = "#3399ff"
fig_data.append(go.Scatter(
x = x,
y = y,
name = 'Observed',
mode = "markers",
opacity = 0.75,
marker = dict(size=10,
color=clr)
)
)
qh = str(qh)
if qh[-1] == '1' and qh != '11':
tname = qh + 'st quantile, pseudo R\u00B2 = ' + pr2_hi
elif qh[-1] == '2':
tname = qh + 'nd quantile, pseudo R\u00B2 = ' + pr2_hi
elif qh[-1] == '3':
tname = qh + 'rd quantile, pseudo R\u00B2 = ' + pr2_hi
else:
tname = qh + 'th quantile, pseudo R\u00B2 = ' + pr2_hi
fig_data.append(go.Scatter(
x = x_p,
y = y_hi,
name = tname,
mode = "lines",
opacity = 0.75,
line = dict(width=3,
dash='dash',
color="#0047b3")
)
)
fig_data.append(
go.Scatter(
x = x_p,
y = y_50,
mode = "lines",
name = 'Median (50th quantile):<br> pseudo R\u00B2 = ' + pr2_50 + '<br> obs vs pred r\u00B2 = ' + r2_50,
opacity = 0.75,
line = dict(width=3,
dash='dash',
color="#ff0000")
)
)
ql = str(ql)
if ql[-1] == '1' and ql != '11':
tname = ql + 'st quantile, R\u00B2 = ' + pr2_lo
elif ql[-1] == '2':
tname = ql + 'nd quantile, R\u00B2 = ' + pr2_lo
elif ql[-1] == '3':
tname = ql + 'rd quantile, R\u00B2 = ' + pr2_lo
else:
tname = ql + 'th quantile, R\u00B2 = ' + pr2_lo
fig_data.append(go.Scatter(
x = x_p,
y = y_lo,
name = tname,
mode = "lines",
opacity = 0.75,
line = dict(width=3,
dash='dash',
color="#0066ff")
)
)
######################################### Lower quantile ###################################
results_summary = res_all[0].summary()
results_as_html1 = results_summary.tables[0].as_html()
df1_summary = pd.read_html(results_as_html1)[0]
#df1_summary['index'] = df1_summary.index
df1_summary = df1_summary.astype(str)
col_names = list(df1_summary)
df3 = pd.DataFrame(columns=['Model information', 'Model statistics'])
df3['Model information'] = df1_summary[col_names[0]].astype(str) + ' ' + df1_summary[col_names[1]].astype(str)
df3['Model statistics'] = df1_summary[col_names[2]].astype(str) + ' ' + df1_summary[col_names[3]].astype(str)
#del df3, df1_summary
dashT1 = dash_table.DataTable(
data=df3.to_dict('records'),
columns=[{'id': c, 'name': c} for c in df3.columns],
export_format="csv",
style_table={'height': '250px',
'overflowY': 'auto',
},
style_cell={'padding':'5px',
'minwidth':'140px',
'width':'160px',
'maxwidth':'160px',
'whiteSpace':'normal',
'textAlign': 'center',
},
)
results_as_html2 = results_summary.tables[1].as_html()
df2_summary = pd.read_html(results_as_html2, header=0)[0]
df2_summary.rename(columns={"Unnamed: 0": "Parameter"}, inplace=True)
dashT2 = dash_table.DataTable(
data=df2_summary.to_dict('records'),
columns=[{'id': c, 'name': c} for c in df2_summary.columns],
export_format="csv",
style_table={'height': '200px',
'overflowY': 'auto',
},
style_cell={'padding':'5px',
'minwidth':'140px',
'width':'160px',
'maxwidth':'160px',
'whiteSpace':'normal',
'textAlign': 'center',
},
)
######################################### 50th quantile ###################################
results_summary = res_all[1].summary()
results_as_html1 = results_summary.tables[0].as_html()
df1_summary = pd.read_html(results_as_html1)[0]
#df1_summary['index'] = df1_summary.index
df1_summary = df1_summary.astype(str)
col_names = list(df1_summary)
df3 = pd.DataFrame(columns=['Model information', 'Model statistics'])
df3['Model information'] = df1_summary[col_names[0]].astype(str) + ' ' + df1_summary[col_names[1]].astype(str)
df3['Model statistics'] = df1_summary[col_names[2]].astype(str) + ' ' + df1_summary[col_names[3]].astype(str)
#del df3, df1_summary
dashT3 = dash_table.DataTable(
data=df3.to_dict('records'),
columns=[{'id': c, 'name': c} for c in df3.columns],
export_format="csv",
style_table={'height': '250px',
'overflowY': 'auto',
},
style_cell={'padding':'5px',
'minwidth':'140px',
'width':'160px',
'maxwidth':'160px',
'whiteSpace':'normal',
'textAlign': 'center',
},
)
results_as_html2 = results_summary.tables[1].as_html()
df2_summary = pd.read_html(results_as_html2, header=0)[0]
df2_summary.rename(columns={"Unnamed: 0": "Parameter"}, inplace=True)
dashT4 = dash_table.DataTable(
data=df2_summary.to_dict('records'),
columns=[{'id': c, 'name': c} for c in df2_summary.columns],
export_format="csv",
style_table={'height': '200px',
'overflowY': 'auto',
},
style_cell={'padding':'5px',
'minwidth':'140px',
'width':'160px',
'maxwidth':'160px',
'whiteSpace':'normal',
'textAlign': 'center',
},
)
######################################### Upper quantile ###################################
results_summary = res_all[2].summary()
results_as_html1 = results_summary.tables[0].as_html()
df1_summary = pd.read_html(results_as_html1)[0]
#df1_summary['index'] = df1_summary.index
df1_summary = df1_summary.astype(str)
col_names = list(df1_summary)
df3 = pd.DataFrame(columns=['Model information', 'Model statistics'])
df3['Model information'] = df1_summary[col_names[0]].astype(str) + ' ' + df1_summary[col_names[1]].astype(str)
df3['Model statistics'] = df1_summary[col_names[2]].astype(str) + ' ' + df1_summary[col_names[3]].astype(str)
#del df3, df1_summary
dashT5 = dash_table.DataTable(
data=df3.to_dict('records'),
columns=[{'id': c, 'name': c} for c in df3.columns],
export_format="csv",
style_table={'height': '250px',
'overflowY': 'auto',
},
style_cell={'padding':'5px',
'minwidth':'140px',
'width':'160px',
'maxwidth':'160px',
'whiteSpace':'normal',
'textAlign': 'center',
},
)
results_as_html2 = results_summary.tables[1].as_html()
df2_summary = pd.read_html(results_as_html2, header=0)[0]
df2_summary.rename(columns={"Unnamed: 0": "Parameter"}, inplace=True)
dashT6 = dash_table.DataTable(
data=df2_summary.to_dict('records'),
columns=[{'id': c, 'name': c} for c in df2_summary.columns],
export_format="csv",
style_table={'height': '200px',
'overflowY': 'auto',
},
style_cell={'padding':'5px',
'minwidth':'140px',
'width':'160px',
'maxwidth':'160px',
'whiteSpace':'normal',
'textAlign': 'center',
},
)
figure = go.Figure(
data = fig_data,
layout = go.Layout(
xaxis = dict(
title = dict(
text = "<b>" + xvar + "</b>",
font = dict(
family = '"Open Sans", "HelveticaNeue", "Helvetica Neue",'
" Helvetica, Arial, sans-serif",
size = 18,
),
),
showticklabels = True,
),
yaxis = dict(
title = dict(
text = "<b>" + yvar + "</b>",
font = dict(
family = '"Open Sans", "HelveticaNeue", "Helvetica Neue",'
" Helvetica, Arial, sans-serif",
size = 18,
),
),
showticklabels = True,
),
margin = dict(l=60, r=30, b=10, t=40),
showlegend = True,
height = 400,
paper_bgcolor = "rgb(245, 247, 249)",
plot_bgcolor = "rgb(245, 247, 249)",
),
)
txt = ""
'''
if jarque_bera_p < 0.05:
txt += "non-"
txt += "normally distributed residuals (p = " + str(jarque_bera_p) + "). "
txt += "The Breusch-Pagan test suggests that the residuals are "
if breusch_pagan_p < 0.05:
txt += "not "
txt += "homoskedastic (p = " + str(breusch_pagan_p) + "). "
txt += "The Durbin-Watson statistic indicates "
if durbin_watson < 1.5 or durbin_watson > 2.5:
txt += "non-"
txt += "independent observations (DW = " + str(durbin_watson) + "). "
txt += "The Harvey-Collier test "
if d != 1:
txt += "was not suitable for this analysis. "
elif np.isnan(harvey_collier_p) == True:
txt += "failed to execute. "
elif harvey_collier_p < 0.05:
txt += "indicates the relationship is not linear (p = " + str(harvey_collier_p) + "). "
elif harvey_collier_p >= 0.05:
txt += "indicates the relationship is linear (p = " + str(harvey_collier_p) + "). "
'''
return figure, "", txt, dashT1, dashT2, dashT3, dashT4, dashT5, dashT6