280 XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3
Classical Linear Regression Model (CLRM)
Assumptions
Testing for Multicollinearity
Multicollinearity, where independent variables are highly
correlated and their individual effects become difficult to
distinguish, was assessed using Variance Inflation Factors
(VIFs). VIF values exceeding 1.0 typically signify some
degree of multicollinearity, increasing in severity with
higher values (Ismaeel et al., 2021). In both models, most
VIFs remained below 2.0, indicating low multicollinearity
(Table 5). Variables like total_communications, total_rdin-
vestments, and total_modificationofprocedures showed
moderate values around 2.0, while fncl_lvrg and energy_
efficiency exhibited the lowest, suggesting minimal cor-
relation with others. Overall, while mild multicollinearity
existed, it did not appear severe enough to violate the regres-
sion assumptions, allowing for reliable model estimation.
Testing for Homoscedasticity
The Breusch-Pagan/Cook-Weisberg test verified the
regression model’s homoscedasticity, assuming constant
error variances across independent variables (Grozdić
et al., 2020). The null hypothesis (H0) of constant vari-
ance yielded an F-statistic of 0.86 (p =0.6209), providing
insufficient evidence to reject it (α =0.05). This suggests
a lack of significant heteroskedasticity, with the relatively
low F-statistic and high p-value supporting this conclu-
sion. Visual inspection of the residuals (Figure 2) further
corroborates the findings. Consequently, the data satisfies
the homoscedasticity assumption for this analysis, allowing
for valid regression model estimation.
Testing for Normality
Normal P-P plots and Shapiro-Wilk tests assessed the nor-
mality assumption for the dependent variables, Tobin’s Q
and ROE (see Figures 3, 4, and Table 6). While Tobin’s Q
displayed near normalcy, the Shapiro-Wilk test indicated a
significant deviation from normality for ROE (p-value
0.00001). This non-normality could potentially affect stan-
dard errors and confidence intervals, impacting statistical
inferences (Fan et al., 2017). However, panel data regression
models are often robust to non-normality due to the pres-
ence of multiple observations per unit (Fan et al., 2017). To
address potential concerns, subsequent regression models
in this study employed robust standard errors to mitigate
the impact of non-normality on statistical inferences.
Hypotheses Testing and Analysis (ROA)
A staged approach tested the hypothesis of an associa-
tion between sustainability behaviours and ROA. First,
a fixed effects panel regression examined the relationship
with non-sustainability variables. Next, an entity-and-time
fixed effects regression incorporated sustainability vari-
ables, controlling for both entity and time-specific effects
for a nuanced analysis. Finally, a fixed effects regression
with multi-way clustering addressed potential data correla-
tions, enhancing robustness. Robustness checks confirmed
Table 3. Descriptive statistics of variables
Variable Description Obs Mean Std. Dev. Min Max
return on asset Return on Assets 97 5.141 9.385 –15.381 43.046
tobin q ratio Tobin Q 97 1.207 0.429 0.404 2.465
fncl lvrg Financial Leverage 97 2.004 0.543 1.069 3.744
size Size 97 9.606 1.139 6.907 11.686
energy efficiency Energy Efficiency 97 –0.067 0.251 –0.657 0.978
commod Mineral commodity 97 2.09 0.579 1 3
total adoptofstand~s Total Adoption of Standards and Rules 97 0.062 0.242 0 1
total associations Total Associations 97 0.732 1.132 0 5
total communications Total Communications 97 0.784 1.244 0 5
total donationfund~s Total Donations and Fundings 97 1.825 1.658 0 8
total assetmodific~s Total Asset Modifications 97 0.701 1.378 0 9
total incentives Total Incentives 97 0.031 0.226 0 2
total modification~s Total Modifications of Procedures 97 1.392 1.538 0 7
total newproducts Total New Products 97 0.062 0.377 0 3
total orgstructuring Total Organizational Structuring 97 0.175 0.5 0 3
total rdinvestments Total Research and Development (R&D) Investments 97 0.32 0.811 0 5
total training Total Training 97 0.804 1.204 0 6
total volunteerism Total Volunteerism 97 0.134 0.372 0 2
total assess measu~t Total Assessment Measurements 97 1.464 1.621 0 7
Classical Linear Regression Model (CLRM)
Assumptions
Testing for Multicollinearity
Multicollinearity, where independent variables are highly
correlated and their individual effects become difficult to
distinguish, was assessed using Variance Inflation Factors
(VIFs). VIF values exceeding 1.0 typically signify some
degree of multicollinearity, increasing in severity with
higher values (Ismaeel et al., 2021). In both models, most
VIFs remained below 2.0, indicating low multicollinearity
(Table 5). Variables like total_communications, total_rdin-
vestments, and total_modificationofprocedures showed
moderate values around 2.0, while fncl_lvrg and energy_
efficiency exhibited the lowest, suggesting minimal cor-
relation with others. Overall, while mild multicollinearity
existed, it did not appear severe enough to violate the regres-
sion assumptions, allowing for reliable model estimation.
Testing for Homoscedasticity
The Breusch-Pagan/Cook-Weisberg test verified the
regression model’s homoscedasticity, assuming constant
error variances across independent variables (Grozdić
et al., 2020). The null hypothesis (H0) of constant vari-
ance yielded an F-statistic of 0.86 (p =0.6209), providing
insufficient evidence to reject it (α =0.05). This suggests
a lack of significant heteroskedasticity, with the relatively
low F-statistic and high p-value supporting this conclu-
sion. Visual inspection of the residuals (Figure 2) further
corroborates the findings. Consequently, the data satisfies
the homoscedasticity assumption for this analysis, allowing
for valid regression model estimation.
Testing for Normality
Normal P-P plots and Shapiro-Wilk tests assessed the nor-
mality assumption for the dependent variables, Tobin’s Q
and ROE (see Figures 3, 4, and Table 6). While Tobin’s Q
displayed near normalcy, the Shapiro-Wilk test indicated a
significant deviation from normality for ROE (p-value
0.00001). This non-normality could potentially affect stan-
dard errors and confidence intervals, impacting statistical
inferences (Fan et al., 2017). However, panel data regression
models are often robust to non-normality due to the pres-
ence of multiple observations per unit (Fan et al., 2017). To
address potential concerns, subsequent regression models
in this study employed robust standard errors to mitigate
the impact of non-normality on statistical inferences.
Hypotheses Testing and Analysis (ROA)
A staged approach tested the hypothesis of an associa-
tion between sustainability behaviours and ROA. First,
a fixed effects panel regression examined the relationship
with non-sustainability variables. Next, an entity-and-time
fixed effects regression incorporated sustainability vari-
ables, controlling for both entity and time-specific effects
for a nuanced analysis. Finally, a fixed effects regression
with multi-way clustering addressed potential data correla-
tions, enhancing robustness. Robustness checks confirmed
Table 3. Descriptive statistics of variables
Variable Description Obs Mean Std. Dev. Min Max
return on asset Return on Assets 97 5.141 9.385 –15.381 43.046
tobin q ratio Tobin Q 97 1.207 0.429 0.404 2.465
fncl lvrg Financial Leverage 97 2.004 0.543 1.069 3.744
size Size 97 9.606 1.139 6.907 11.686
energy efficiency Energy Efficiency 97 –0.067 0.251 –0.657 0.978
commod Mineral commodity 97 2.09 0.579 1 3
total adoptofstand~s Total Adoption of Standards and Rules 97 0.062 0.242 0 1
total associations Total Associations 97 0.732 1.132 0 5
total communications Total Communications 97 0.784 1.244 0 5
total donationfund~s Total Donations and Fundings 97 1.825 1.658 0 8
total assetmodific~s Total Asset Modifications 97 0.701 1.378 0 9
total incentives Total Incentives 97 0.031 0.226 0 2
total modification~s Total Modifications of Procedures 97 1.392 1.538 0 7
total newproducts Total New Products 97 0.062 0.377 0 3
total orgstructuring Total Organizational Structuring 97 0.175 0.5 0 3
total rdinvestments Total Research and Development (R&D) Investments 97 0.32 0.811 0 5
total training Total Training 97 0.804 1.204 0 6
total volunteerism Total Volunteerism 97 0.134 0.372 0 2
total assess measu~t Total Assessment Measurements 97 1.464 1.621 0 7