Naldi Carrion - Fab Lab ESAN - Fab Futures - Data Science

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Week 2 - 1st Class: Fitting

This class aim was to learn model fitting concept = find a function that could represent as good as possible every point of data in two ways:

• Interpolation: the curve passes exactly through all points.
• Approximation/regression: the curve approximates as closely as possible, but does not necessarily pass through all points.

We can use Python to processes:

• Lineal Fitting lineal
• Polinomic Fitting
• Diference between underfitting and overfitting
• Using scipy.optimize.curve_fit
• Visualizing outputs
• Interpretation of metrics

The higher the degree of a polynomial, the more it can be bent to "fit.". When we have a very complex polynomial can pass through all the points (exact interpolation), but it becomes unstable. It introduces the concept of overfitting which results in a useless model.

Using Python to Model Fitting

The class uses Python with libraries such as numpy, matplotlib y panda.

• Numpy: Use for numerical math, especially with arrays (vectors and matrices). We can use it for:

  • Creating number sequences (np.linspace).
  • Performing mathematical operations very quickly.
  • Generating noise, distributions, and random values.
  • Working with matrices (foundation of machine learning).
  • Performing linear algebra: multiplications, eigenvalues, etc.
  • Converting data into machine-readable formats.

• Matplot: Basic library for drawing graphs in Python. We can use it for:

  • Graphing points, lines, bars, pie charts, and histograms.
  • Visualizing data before modeling.
  • Comparing model results.
  • Viewing errors, dispersion, and trends.
  • Documenting your experimental or scientific process.

• Pandas: Python library designed to work with tabular data, we can use it for read:

  • Excel spreadsheet
  • SQL table
  • CSV file
  • A survey
  • A sensor dataset
  • A lab file

I will use them for an exercise

Artificial Data Creation

I try to run a code to create random data:

• x → will create 10 points between -1 and 1. Using linspace(-1, 1, 10)
• y → generates values that approximately follow the function y = x, but adding noise. Using 0.1 * np.random.randn(10) It will generate 10 random numbers with a normal distribution (mean 0 and variance 1), but multiplied by 0.1 so that the "noise" is small.

import numpy as np

x = np.linspace(-1, 1, 10)
y = x + 0.1*np.random.randn(10)

print(x)
print(y)

[-1.         -0.77777778 -0.55555556 -0.33333333 -0.11111111  0.11111111
  0.33333333  0.55555556  0.77777778  1.        ]
[-0.88833741 -0.76938407 -0.50452391 -0.3598181  -0.13191568  0.18267083
  0.32884573  0.42656282  0.70169181  1.01129203]

And we can also plot both values (x,y) using matplot library

import matplotlib.pyplot as plt

x = np.linspace(-1, 1, 10)
y = x + 0.1*np.random.randn(10)

plt.scatter(x, y)
plt.show()

Adjusting a Polinomial

We need to find the coefficients of a polynomial of degree deg that best fits the points. Using the previous example we will create a 10 points data set using the np.linspace command. Then We nned to use the polynomial function p = np.polyfit(x, y, deg) where we will need to define the polynomial grade. Then I will need to create more points for X to graphic the polynomial. Then to graphic both (original data and the plynomial) we can use plt.scatter(...) and plt.plot(...)

import numpy as np
import matplotlib.pyplot as plt

# 1. datos del ejemplo anterior
x = np.linspace(-1, 1, 10)
y = x + 0.1*np.random.randn(10)

# 2. Solicitar ajustar un polinomio grado 1
deg = 1
p = np.polyfit(x, y, deg)

# 3. Crear un conjunto más fino de x para dibujar la curva suave
xp = np.linspace(-1, 1, 100)
yp = np.polyval(p, xp)

# 4. Graficar
plt.figure(figsize=(8,5))
plt.scatter(x, y, color='blue', label='Original Data')
plt.plot(xp, yp, color='red', label='Polynomial Adjust (grade 1)')
plt.legend()
plt.title("Polynomial Adjust grade 1")
plt.xlabel("x")
plt.ylabel("y")

plt.show()

import numpy as np
import matplotlib.pyplot as plt

# 1. datos del ejemplo anterior
x = np.linspace(-1, 1, 10)
y = x + 0.1*np.random.randn(10)

# 2. Solicitar ajustar un polinomio grado 5
deg = 5
p = np.polyfit(x, y, deg)

# 3. Crear un conjunto más fino de x para dibujar la curva suave
xp = np.linspace(-1, 1, 100)
yp = np.polyval(p, xp)

# 4. Graficar
plt.figure(figsize=(8,5))
plt.scatter(x, y, color='blue', label='Original Data')
plt.plot(xp, yp, color='red', label='Polynomial Adjust (grade 5)')
plt.legend()
plt.title("Polynomial Adjust grade 5")
plt.xlabel("x")
plt.ylabel("y")

plt.show()

Trying libraries with my Data

I will use my thesis pilot data to run test some relationships, trying to summarize the main visual analysis from my PhD pilot survey with entrepreneurs. It focuses on three latent variables:

• Frugality (FRUG)
• Entrepreneurial Bricolage (BRIC)
• Innovative Behaviour (INNOV) The goal is to create clear, reproducible plots and simple models that I can use in my final presentation.

1. Setup and libraries

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt

import statsmodels.api as sm
import networkx as nx

from sklearn.cross_decomposition import PLSRegression

# Optional: make plots a bit larger by default
plt.rcParams['figure.figsize'] = (8, 5)

# Show plots inside the notebook (Jupyter)
%matplotlib inline

2. Loading the pilot survey data

The dataset comes from the pilot survey with entrepreneurs and is stored as a CSV file.

• File: datasets/2nd_Class_Assignmt_Data/Entrepreneurs.csv
• Separator: semicolon (;)
  Each row is one entrepreneur, each column is an item or variable (socio-demographic, FRUG, BRIC, INNOV, etc.).

import pandas as pd

df = pd.read_csv("datasets/2nd_Class_Assignmt_Data/Entrepreneurs.csv", sep=";")
df.head()

	Marca temporal	NOM	GEN	EAGE	FOUND	CAGE1	AFOUND	CBASED	CSECT	EEXP	...	INNOV2	INNOV3	INNOV4	CAGE2	TECHBS	ETEAM	EAOS	SEEDF	OPERF	INCC
0	4/4/2025 18:10:28	iFurniture	2	35	1	2	1	2	9	1	...	4	2	4	1	1	1	1	1	1	1
1	4/6/2025 13:09:46	Salvy Natural - Indes Perú	2	37	1	2	1	2	12	1	...	5	5	5	1	1	1	1	0	0	0
2	4/7/2025 16:07:37	AVR Technology	1	23	1	2	1	2	15	0	...	4	4	4	0	1	1	1	1	1	1
3	4/7/2025 21:49:59	AIO SENSORS	1	32	1	1	1	3	9	0	...	4	4	4	0	1	1	1	0	1	1
4	4/8/2025 17:54:07	Face Me	1	30	1	2	1	3	5	0	...	4	4	4	1	1	0	1	1	1	1

5 rows × 41 columns

# Loading the original dataset
df = pd.read_csv("datasets/2nd_Class_Assignmt_Data/Entrepreneurs.csv", sep=";")

print("Shape of full dataset:", df.shape)
df.head()

Shape of full dataset: (39, 41)

	Marca temporal	NOM	GEN	EAGE	FOUND	CAGE1	AFOUND	CBASED	CSECT	EEXP	...	INNOV2	INNOV3	INNOV4	CAGE2	TECHBS	ETEAM	EAOS	SEEDF	OPERF	INCC
0	4/4/2025 18:10:28	iFurniture	2	35	1	2	1	2	9	1	...	4	2	4	1	1	1	1	1	1	1
1	4/6/2025 13:09:46	Salvy Natural - Indes Perú	2	37	1	2	1	2	12	1	...	5	5	5	1	1	1	1	0	0	0
2	4/7/2025 16:07:37	AVR Technology	1	23	1	2	1	2	15	0	...	4	4	4	0	1	1	1	1	1	1
3	4/7/2025 21:49:59	AIO SENSORS	1	32	1	1	1	3	9	0	...	4	4	4	0	1	1	1	0	1	1
4	4/8/2025 17:54:07	Face Me	1	30	1	2	1	3	5	0	...	4	4	4	1	1	0	1	1	1	1

5 rows × 41 columns

3. Filtering active entrepreneurs

I keep only those respondents who continue actively working on their venture I filtered my data using only those that answered that they continue actively working on their business initiative (AFOUND = 1).:

• Column AFOUND
  • ¿Continúas impulsando (trabajando/desarrollando) tu emprendimiento/proyecto?
    • Si = 1 (1 = still working on the venture)
    • No = 0 (0 = not active anymore)

Thus, I need to differenciate between entrepreneurs, those that answered "Yes" and bring intructions to split the data for the análisis. Hence I need to create a data frame (df_active), that will look for those answers that in collum labeled as "AFOUND" contain the number "1". The result is shown in the following box that reduce the answers under analysis to 37, from the 39 that compound my pilot survey. This creates a filtered dataset df_active that I use for the rest of the analysis.

I needed to create a boolean mask, creating a true/false recognition within the AFOUND column list,selecting those meeting the condition. And I have to add copy() to avoid any confusion with the first dataframe

• Here is the first code I used: ```df_active = df[df["AFOUND"] == 1].copy()
• Then I added a line to execute the coding: ```df_active.head(), df_active.shape

df_active = df[df["AFOUND"] == 1].copy()
df_active.head(), df_active.shape

(      Marca temporal                          NOM  GEN  EAGE  FOUND  CAGE1  \
 0  4/4/2025 18:10:28                  iFurniture     2    35      1      2   
 1  4/6/2025 13:09:46  Salvy Natural - Indes Perú     2    37      1      2   
 2  4/7/2025 16:07:37               AVR Technology    1    23      1      2   
 3  4/7/2025 21:49:59                 AIO SENSORS     1    32      1      1   
 4  4/8/2025 17:54:07                      Face Me    1    30      1      2   
 
    AFOUND  CBASED  CSECT  EEXP  ...  INNOV2  INNOV3  INNOV4  CAGE2  TECHBS  \
 0       1       2      9     1  ...       4       2       4      1       1   
 1       1       2     12     1  ...       5       5       5      1       1   
 2       1       2     15     0  ...       4       4       4      0       1   
 3       1       3      9     0  ...       4       4       4      0       1   
 4       1       3      5     0  ...       4       4       4      1       1   
 
    ETEAM  EAOS  SEEDF  OPERF  INCC  
 0      1     1      1      1     1  
 1      1     1      0      0     0  
 2      1     1      1      1     1  
 3      1     1      0      1     1  
 4      0     1      1      1     1  
 
 [5 rows x 41 columns],
 (37, 41))

# Filter only active founders (AFOUND == 1)
df_active = df[df["AFOUND"] == 1].copy()

print("Shape of active-founders dataset:", df_active.shape)
df_active.head()

Shape of active-founders dataset: (37, 41)

	Marca temporal	NOM	GEN	EAGE	FOUND	CAGE1	AFOUND	CBASED	CSECT	EEXP	...	INNOV2	INNOV3	INNOV4	CAGE2	TECHBS	ETEAM	EAOS	SEEDF	OPERF	INCC
0	4/4/2025 18:10:28	iFurniture	2	35	1	2	1	2	9	1	...	4	2	4	1	1	1	1	1	1	1
1	4/6/2025 13:09:46	Salvy Natural - Indes Perú	2	37	1	2	1	2	12	1	...	5	5	5	1	1	1	1	0	0	0
2	4/7/2025 16:07:37	AVR Technology	1	23	1	2	1	2	15	0	...	4	4	4	0	1	1	1	1	1	1
3	4/7/2025 21:49:59	AIO SENSORS	1	32	1	1	1	3	9	0	...	4	4	4	0	1	1	1	0	1	1
4	4/8/2025 17:54:07	Face Me	1	30	1	2	1	3	5	0	...	4	4	4	1	1	0	1	1	1	1

5 rows × 41 columns

4. Building latent-variable mean scores

The questionnaire includes multiple Likert-scale items for each construct:

• Frugality: FRUG1 to FRUG7
• Bricolage: BRIC1 to BRIC8
• Innovative Behaviour: INNOV1 to INNOV4

I compute a simple mean score per respondent for each construct, creating:

• FRUG_mean
• BRIC_mean
• INNOV_mean

import pandas as pd

df = pd.read_csv("datasets/2nd_Class_Assignmt_Data/Entrepreneurs.csv", sep=";")
df_active = df[df["AFOUND"] == 1].copy()
df_active.head(), df_active.shape

# Listas de items
frug_items  = [f'FRUG{i}' for i in range(1, 8)]
bric_items  = [f'BRIC{i}' for i in range(1, 9)]
innov_items = [f'INNOV{i}' for i in range(1, 5)]

# Mean scores
df_active['FRUG_mean']  = df_active[frug_items].mean(axis=1)
df_active['BRIC_mean']  = df_active[bric_items].mean(axis=1)
df_active['INNOV_mean'] = df_active[innov_items].mean(axis=1)

df_active[['FRUG_mean','BRIC_mean','INNOV_mean']].head()

	FRUG_mean	BRIC_mean	INNOV_mean
0	5.000000	4.125	3.25
1	3.571429	4.750	5.00
2	4.000000	4.000	4.00
3	4.000000	4.375	4.00
4	4.285714	4.375	4.00

5. Distributions of latent-variable scores

To see how the constructs are distributed among active entrepreneurs, I plot histograms for each mean score.

import matplotlib.pyplot as plt

plt.figure(figsize=(12, 8))

# FRUG
plt.subplot(3, 1, 1)
plt.hist(df_active['FRUG_mean'], bins=10, edgecolor='black')
plt.title("Frugality (FRUG_mean)")

# BRIC
plt.subplot(3, 1, 2)
plt.hist(df_active['BRIC_mean'], bins=10, edgecolor='black')
plt.title("Bricolage (BRIC_mean)")

# INNOV
plt.subplot(3, 1, 3)
plt.hist(df_active['INNOV_mean'], bins=10, edgecolor='black')
plt.title("Innovation (INNOV_mean)")

plt.tight_layout()
plt.show()

6. Pairwise relationships (scatter plots)

Next, I visualize the pairwise relationships between the constructs:

1. Frugality → Bricolage
2. Bricolage → Innovation
3. Frugality → Innovation

plt.scatter(df_active['FRUG_mean'], df_active['BRIC_mean'])
plt.xlabel("Frugality (FRUG_mean)")
plt.ylabel("Bricolage (BRIC_mean)")
plt.title("Scatterplot: Frugality → Bricolage")
plt.show()

plt.scatter(df_active['BRIC_mean'], df_active['INNOV_mean'])
plt.xlabel("Bricolage (BRIC_mean)")
plt.ylabel("Innovation (INNOV_mean)")
plt.title("Scatterplot: Bricolage → Innovation")
plt.show()

plt.scatter(df_active['FRUG_mean'], df_active['INNOV_mean'])
plt.xlabel("Frugality (FRUG_mean)")
plt.ylabel("Innovation (INNOV_mean)")
plt.title("Scatterplot: Frugality → Innovation")
plt.show()

6. Now we need to apply fitting

7. Simple linear fits and R²

For each relationship, I estimate a simple linear regression using numpy.polyfit:

• I obtain the line: y = a * x + b
• I compute and report the R² manually.

• Fitting: Frugality → Bricolage

import numpy as np
import matplotlib.pyplot as plt

# Variables
x = df_active['FRUG_mean']
y = df_active['BRIC_mean']

# Linear fit
coef = np.polyfit(x, y, 1)
model = np.poly1d(coef)

# Plot
plt.scatter(x, y)
plt.plot(x, model(x), color='red')
plt.xlabel("Frugality (FRUG_mean)")
plt.ylabel("Bricolage (BRIC_mean)")
plt.title("Linear Fit: Frugality → Bricolage")
plt.show()

# Print model
coef

array([-0.0251913 ,  4.41082375])

• we need to calculate R¨2

y_pred = model(x)
SS_res = np.sum((y - y_pred)**2)
SS_tot = np.sum((y - np.mean(y))**2)
R2 = 1 - (SS_res / SS_tot)
R2

np.float64(0.0014589990012413567)

• Fitting: Bricolage → Innovation

x = df_active['BRIC_mean']
y = df_active['INNOV_mean']

coef = np.polyfit(x, y, 1)
model = np.poly1d(coef)

plt.scatter(x, y)
plt.plot(x, model(x), color='red')
plt.xlabel("Bricolage (BRIC_mean)")
plt.ylabel("Innovation (INNOV_mean)")
plt.title("Linear Fit: Bricolage → Innovation")
plt.show()

# R²
y_pred = model(x)
SS_res = np.sum((y - y_pred)**2)
SS_tot = np.sum((y - np.mean(y))**2)
R2 = 1 - (SS_res / SS_tot)
R2

np.float64(0.11605670441386895)

• Fitting: Frugality → Innovation

x = df_active['FRUG_mean']
y = df_active['INNOV_mean']

coef = np.polyfit(x, y, 1)
model = np.poly1d(coef)

plt.scatter(x, y)
plt.plot(x, model(x), color='red')
plt.xlabel("Frugality (FRUG_mean)")
plt.ylabel("Innovation (INNOV_mean)")
plt.title("Linear Fit: Frugality → Innovation")
plt.show()

# R²
y_pred = model(x)
SS_res = np.sum((y - y_pred)**2)
SS_tot = np.sum((y - np.mean(y))**2)
R2 = 1 - (SS_res / SS_tot)
R2

np.float64(0.07432234697273854)

8. Internal reliability – Cronbach’s alpha

To check internal consistency of each scale, I compute Cronbach’s alpha:

• Values around 0.70 – 0.80 are typically considered acceptable in early-stage research.

import numpy as np

def cronbach_alpha(df_items):
    df_items = df_items.dropna()  # por seguridad
    item_vars = df_items.var(axis=0, ddof=1)
    total_var = df_items.sum(axis=1).var(ddof=1)
    n_items = df_items.shape[1]
    alpha = (n_items / (n_items - 1)) * (1 - item_vars.sum() / total_var)
    return alpha

frug_items  = [f'FRUG{i}' for i in range(1, 8)]
bric_items  = [f'BRIC{i}' for i in range(1, 9)]
innov_items = [f'INNOV{i}' for i in range(1, 5)]

alpha_frug = cronbach_alpha(df_active[frug_items])
alpha_frug

np.float64(0.7970463064738873)

alpha_bric = cronbach_alpha(df_active[bric_items])
alpha_bric

np.float64(0.7196649161227224)

alpha_innov = cronbach_alpha(df_active[innov_items])
alpha_innov

np.float64(0.7246906066139176)

9. Simple path diagram (visual summary)

Using the coefficients from the linear fits, I draw a simple path diagram with:

• Nodes: Frugality, Bricolage, Innovation
• Directed arrows: using the path coefficients from the linear fits.

import networkx as nx
import matplotlib.pyplot as plt

G = nx.DiGraph()

G.add_edge("Frugality", "Bricolage", weight=-0.025)
G.add_edge("Bricolage", "Innovation", weight=0.116)
G.add_edge("Frugality", "Innovation", weight=-0.074)

pos = {
    "Frugality": (0, 1),
    "Bricolage": (1, 1),
    "Innovation": (1, 0)
}

plt.figure(figsize=(8,6))
nx.draw(G, pos, with_labels=True, node_size=4000, node_color="lightblue", font_size=12, arrowsize=20)

labels = {
    ("Frugality", "Bricolage"): "-0.025",
    ("Bricolage", "Innovation"): "0.116",
    ("Frugality", "Innovation"): "-0.074"
}

nx.draw_networkx_edge_labels(G, pos, edge_labels=labels, font_color='red')
plt.title("Path Model: Frugality, Bricolage and Innovation")
plt.show()

10. Moderation model: FRUG × BRIC

To explore a simple moderation, I create an interaction term:

• interaction = FRUG_mean * BRIC_mean

Then I estimate an Ordinary Least Squares (OLS) model:

Y=β0​+β1​X1​+β2​X2​+β3​(X1​X2​)+ε

INNOV_mean = β0​+β1​FRUG_mean​+β2​BRIC_mean​+β3​(FRUG_mean​BRIC_mean​)+ε

This is mainly exploratory in the pilot stage.

import statsmodels.api as sm
import pandas as pd

# Crear el término de interacción
df_active['interaction'] = df_active['FRUG_mean'] * df_active['BRIC_mean']

# Variables independientes
X = df_active[['FRUG_mean', 'BRIC_mean', 'interaction']]
X = sm.add_constant(X)

# Variable dependiente
y = df_active['INNOV_mean']

# Ajustar modelo lineal
model = sm.OLS(y, X).fit()
print(model.summary())

                            OLS Regression Results                            
==============================================================================
Dep. Variable:             INNOV_mean   R-squared:                       0.215
Model:                            OLS   Adj. R-squared:                  0.144
Method:                 Least Squares   F-statistic:                     3.012
Date:                Sun, 30 Nov 2025   Prob (F-statistic):             0.0439
Time:                        05:17:11   Log-Likelihood:                -33.254
No. Observations:                  37   AIC:                             74.51
Df Residuals:                      33   BIC:                             80.95
Df Model:                           3                                         
Covariance Type:            nonrobust                                         
===============================================================================
                  coef    std err          t      P>|t|      [0.025      0.975]
-------------------------------------------------------------------------------
const         -10.1494     11.465     -0.885      0.382     -33.476      13.177
FRUG_mean       2.9300      2.812      1.042      0.305      -2.790       8.650
BRIC_mean       3.6296      2.679      1.355      0.185      -1.822       9.081
interaction    -0.7554      0.658     -1.149      0.259      -2.093       0.582
==============================================================================
Omnibus:                        2.448   Durbin-Watson:                   1.809
Prob(Omnibus):                  0.294   Jarque-Bera (JB):                1.966
Skew:                          -0.562   Prob(JB):                        0.374
Kurtosis:                       2.896   Cond. No.                     2.21e+03
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 2.21e+03. This might indicate that there are
strong multicollinearity or other numerical problems.

11. PLS-style analysis (FRUG, BRIC, INNOV)

As a very simple PLS-SEM style check, I:

1. Build latent variable scores as means: FRUG_LV, BRIC_LV, INNOV_LV
2. Estimate:
   • Model 1: FRUG → BRIC
   • Model 2: FRUG + BRIC → INNOV

This is just an exploratory step to see the direction and intensity of paths.

from sklearn.cross_decomposition import PLSRegression
from sklearn.preprocessing import StandardScaler
import numpy as np
import pandas as pd

# 1. Definir ítems
frug_items  = [f'FRUG{i}' for i in range(1, 8)]
bric_items  = [f'BRIC{i}' for i in range(1, 9)]
innov_items = [f'INNOV{i}' for i in range(1, 5)]

# 2. Estandarizar indicadores
scaler = StandardScaler()
df_z = pd.DataFrame(
    scaler.fit_transform(df_active[frug_items + bric_items + innov_items]),
    columns = frug_items + bric_items + innov_items
)

# 3. LVs como promedio estandarizado
df_active['FRUG_LV']  = df_z[frug_items].mean(axis=1)
df_active['BRIC_LV']  = df_z[bric_items].mean(axis=1)
df_active['INNOV_LV'] = df_z[innov_items].mean(axis=1)

# 4. DataFrame sin NaN
df_pls = df_active[['FRUG_LV', 'BRIC_LV', 'INNOV_LV']].dropna()

print("N original:", len(df_active))
print("N sin NaN (para PLS):", len(df_pls))

# ========== MODELO PLS 1: FRUG → BRIC ==========
X1 = df_pls[['FRUG_LV']].values           # (n, 1)
Y1 = df_pls[['BRIC_LV']].values           # (n, 1)

pls1 = PLSRegression(n_components=1)
pls1.fit(X1, Y1)

# ========== MODELO PLS 2: FRUG + BRIC → INNOV ==========
X2 = df_pls[['FRUG_LV', 'BRIC_LV']].values   # (n, 2)
Y2 = df_pls[['INNOV_LV']].values            # (n, 1)

pls2 = PLSRegression(n_components=1)
pls2.fit(X2, Y2)

print("\nShape coef_ pls2:", pls2.coef_.shape)
print("Matriz coef_ pls2:\n", pls2.coef_)

coef_frug = pls2.coef_[0, 0]  # FRUG → INNOV
coef_bric = pls2.coef_[0, 1]  # BRIC → INNOV

print("\nPath coefficients:")
print("FRUG → BRIC:",  pls1.coef_[0, 0])
print("FRUG → INNOV:", coef_frug)
print("BRIC → INNOV:", coef_bric)

print("\nR²:")
print("R² BRIC  =", pls1.score(X1, Y1))
print("R² INNOV =", pls2.score(X2, Y2))

N original: 37
N sin NaN (para PLS): 35

Shape coef_ pls2: (1, 2)
Matriz coef_ pls2:
 [[-0.27767944  0.41300091]]

Path coefficients:
FRUG → BRIC: -0.07999765255262897
FRUG → INNOV: -0.2776794381003554
BRIC → INNOV: 0.41300091261055083

R²:
R² BRIC  = 0.010180442019163016
R² INNOV = 0.17567543689134357

df_active[['FRUG_LV', 'BRIC_LV', 'INNOV_LV']].isna().sum()

FRUG_LV     2
BRIC_LV     2
INNOV_LV    2
dtype: int64

df_active[df_active[['FRUG_LV','BRIC_LV','INNOV_LV']].isna().any(axis=1)]

	Marca temporal	NOM	GEN	EAGE	FOUND	CAGE1	AFOUND	CBASED	CSECT	EEXP	...	SEEDF	OPERF	INCC	FRUG_mean	BRIC_mean	INNOV_mean	interaction	FRUG_LV	BRIC_LV	INNOV_LV
37	7/25/2025 19:15:51	Glexco Robotics and Automation	1	55	1	1	1	3	15	0	...	0	0	0	4.428571	4.00	5.0	17.714286	NaN	NaN	NaN
38	7/27/2025 3:40:23	UMA	2	25	1	2	1	2	3	0	...	0	1	1	4.285714	4.75	3.0	20.357143	NaN	NaN	NaN

2 rows × 48 columns

df_active.loc[[37, 38], frug_items + bric_items + innov_items]

	FRUG1	FRUG2	FRUG3	FRUG4	FRUG5	FRUG6	FRUG7	BRIC1	BRIC2	BRIC3	BRIC4	BRIC5	BRIC6	BRIC7	BRIC8	INNOV1	INNOV2	INNOV3	INNOV4
37	5	5	4	3	4	5	5	4	4	3	4	5	4	4	4	5	5	5	5
38	5	5	4	3	4	4	5	5	5	5	5	3	5	5	5	5	1	5	1

df_active.loc[[37, 38], frug_items].std(axis=1)
df_active.loc[[37, 38], bric_items].std(axis=1)
df_active.loc[[37, 38], innov_items].std(axis=1)

37    0.000000
38    2.309401
dtype: float64

# Construir LVs como promedios simples
df_active['FRUG_LV']  = df_active[frug_items].mean(axis=1)
df_active['BRIC_LV']  = df_active[bric_items].mean(axis=1)
df_active['INNOV_LV'] = df_active[innov_items].mean(axis=1)

# Ahora ya no habrá NaN
df_active[['FRUG_LV', 'BRIC_LV', 'INNOV_LV']].isna().sum()
# debería dar 0 en las tres

# Y el PLS se hace con los 37 casos:
df_pls = df_active[['FRUG_LV', 'BRIC_LV', 'INNOV_LV']]  # sin dropna

from sklearn.cross_decomposition import PLSRegression
import numpy as np

X1 = df_pls[['FRUG_LV']].values
Y1 = df_pls[['BRIC_LV']].values
pls1 = PLSRegression(n_components=1).fit(X1, Y1)

X2 = df_pls[['FRUG_LV', 'BRIC_LV']].values
Y2 = df_pls[['INNOV_LV']].values
pls2 = PLSRegression(n_components=1).fit(X2, Y2)

print("FRUG → BRIC:",  pls1.coef_[0, 0])
print("FRUG → INNOV:", pls2.coef_[0, 0])
print("BRIC → INNOV:", pls2.coef_[0, 1])
print("R² BRIC =",  pls1.score(X1, Y1))
print("R² INNOV =", pls2.score(X2, Y2))

FRUG → BRIC: -0.02519129956878327
FRUG → INNOV: -0.2969265226888666
BRIC → INNOV: 0.5626020708431478
R² BRIC = 0.0014589990012412457
R² INNOV = 0.18353896726416463

12. Short interpretation notes

• Scale reliability: Cronbach’s alpha values are acceptable for an early-stage pilot.
• Relationships: Bricolage tends to have a more positive link with Innovation than Frugality does.
• Frugality: In this small sample, frugality shows a weak or even slightly negative direct association with innovation, which is interesting for my theoretical discussion.
• Pilot nature: All results are exploratory and mainly useful to refine hypotheses and the final research design.