ArticlePublisher preview available

Extending El-Hadri-Sahli-Hanafi procedure for path analysis with non standardized variables

Springer Nature
Quality & Quantity
Authors:
Abderrahim Sahli
Abderrahim Sahli
Abderrahim Sahli
  • This person is not on ResearchGate, or hasn't claimed this research yet.
Ebnou Abdem Seyid Abdellahi at Mohammed VI Polytechnic University
Ebnou Abdem Seyid Abdellahi
Mohamed Hanafi
Mohamed Hanafi
Mohamed Hanafi
  • This person is not on ResearchGate, or hasn't claimed this research yet.
El Hadri Zouhair at Mohammed V University
El Hadri Zouhair
Read publisher preview
Download citation
To read the full-text of this research, you can request a copy directly from the authors.

Abstract and Figures

Path analysis is a powerful statistical technique for studying both the direct and indirect causal relationships among observed variables. The estimation step is the core of the whole modeling process. It is conventionally performed using the well-known BFGS procedure, especially when the variables are standardized. Recently, a new alternative procedure has been introduced by El Hadri, Sahli and Hanafi. This new procedure possesses remarkable convergence properties, including monotone convergence and convergence of the error toward zero. Furthermore, it is faster in practice than the BFGS procedure. However, these properties have been proven only in the case of standardized variables. Given that the general case of non standardized variables is more prevalent and important, this limitation hinders its broader application. The present paper extends the new procedure to the case of non standardized variables. On the theoretical level, we show that the monotone convergence and the convergence of the error are maintained. On the practical level, several simulations show that the parameters obtained by the proposed procedure are close to those provided by the R lavaan package.
Figures - available from: Quality & Quantity
This content is subject to copyright. Terms and conditions apply.
A preview of this full-text is provided by Springer Nature.
Learn more
Content available from Quality & Quantity 
This content is subject to copyright. Terms and conditions apply.
Vol.:(0123456789)
Quality & Quantity (2025) 59:175–190
https://doi.org/10.1007/s11135-024-01932-8
Extending El‑Hadri‑Sahli‑Hanafi procedure forpath analysis
withnon standardized variables
AbderrahimSahli1· SeyidAbdellahiEbnouAbdem2 · MohamedHana3·
ZouhairElHadri1
Accepted: 25 June 2024 / Published online: 10 July 2024
© The Author(s), under exclusive licence to Springer Nature B.V. 2024
Abstract
Path analysis is a powerful statistical technique for studying both the direct and indirect
causal relationships among observed variables. The estimation step is the core of the whole
modeling process. It is conventionally performed using the well-known BFGS procedure,
especially when the variables are standardized. Recently, a new alternative procedure has
been introduced by El Hadri, Sahli and Hanafi. This new procedure possesses remarkable
convergence properties, including monotone convergence and convergence of the error
toward zero. Furthermore, it is faster in practice than the BFGS procedure. However, these
properties have been proven only in the case of standardized variables. Given that the gen-
eral case of non standardized variables is more prevalent and important, this limitation
hinders its broader application. The present paper extends the new procedure to the case
of non standardized variables. On the theoretical level, we show that the monotone con-
vergence and the convergence of the error are maintained. On the practical level, several
simulations show that the parameters obtained by the proposed procedure are close to those
provided by the R lavaan package.
Keywords Path analysis· Implied covariance matrix· Finite iterative method· Estimation
of parameters
* Abderrahim Sahli
abderrahimsahli95@gmail.com
Seyid Abdellahi Ebnou Abdem
seyidebnou@gmail.com
Mohamed Hanafi
mohamed.hanafi@oniris-nantes.fr
Zouhair El Hadri
z.elhadri@um5r.ac.ma
1 Mathematics, Statistics, andApplications Laboratory, Faculty ofsciences, Mohammed V
University inRabat, Rabat, Morocco
2 Center ofUrban Systems (CUS), University Mohammed VI Polytechnic (UM6P), Lot 660, Hay
Moulay Rachid, BenGuerir43150, Morocco
3 Research unit inStatistics, Sensometrics andChemometrics, Oniris, Nantes, France
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
... PAM is a set of statistical techniques used to assess the causal relationships between observed variables [30,[39][40][41][42][43]. In other words, PAM is an advanced statistical method for identifying and examining both the direct and indirect causal relationships among a set of exogenous variables (ξ) 3 (independence, predictor, input) [11] and endogenous variables (η) 4 (dependence, output) [11,30]. ...
... PAM can be considered an extension of multiple regression models in the sense that it allows several variables to be dependent. Unlike multiple regression, where only one variable is dependent, PAM permits variables to serve as both causes and effects [30,39,43]. Figure 1 below, which illustrates the limitations of multiple regression models when dealing with multiple intermediate dependent variables or situations where variables form a causal chain (e.g., Z1 depends on Z, which in turn depends on Y). ...
... Figure 1 below, which illustrates the limitations of multiple regression models when dealing with multiple intermediate dependent variables or situations where variables form a causal chain (e.g., Z1 depends on Z, which in turn depends on Y). PAM overcomes these limitations by examining both direct and indirect (intermediate) effects [11,30,41,43]. On the other hand, PAM is a special case of Structural Equation Modeling (SEM) which is a set of related statistical techniques used to evaluate the fit of a hypothesized causal model with available data, the differentiation of PAM from other SEM models is that it concerns the directs and indirect effects only between the observed variables [11,30]. ...
Comparative modeling of household electricity consumption in France: Insights from path analysis and classical models
Article
Full-text available
  • Feb 2025
Electricity consumption in Europe has risen significantly in recent years, with households being the largest consumers of final electricity. Managing and reducing residential power consumption is critical for achieving efficient and sustainable energy management, conserving financial resources, and mitigating environmental effects. Many studies have used statistical models such as linear, multinomial, ridge, polynomial, and LASSO regression to examine and understand the determinants of residential energy consumption. However, these models are limited to capturing only direct effects among the determinants of household energy consumption. This study addresses these limitations by applying a path analysis model that captures the direct and indirect effects. Numerical and theoretical comparisons that demonstrate its advantages and efficiency are also given. The results show that Sub-metering components associated with specific uses, like cooking or water heating, have significant indirect impacts on global intensity through active power and that the voltage affects negatively the global power (active and reactive) due to the physical and behavioral mechanisms. Our findings provide an in-depth understanding of household electricity power consumption. This will improve forecasting and enable real-time energy management tools, extending to the design of precise energy efficiency policies to achieve SDG 7’s objectives.
View
... Consequently, the associated parameters should be estimated by the appropriate strategy. In this regard, El Hadri & al El Hadri et al. (2023); Sahli et al. (2024) recently proposed a new method to estimate such type of models. It consists of an Alternating Least Square procedure based on the Finite Iterative Method El Hadri and Hanafi (2015). ...
Finite Iterative Method Based Algorithm To Estimate Latent Variables For Reflective Blocks In Partial Least Squares Structural Equation Modeling
Article
Full-text available
  • Mar 2025
Partial Least Squares Structural Equation Modeling (PLS-SEM) is a powerful statistical approach that has become a mainstream method in many application areas. It offers flexibility in handling formative and reflective measurement blocks, enabling researchers to model relationships among observed and latent variables. The crucial step in this approach is the PLS-SEM algorithm, which involves computing the scores of latent variables by alternating between inner and outer estimation. The aims of the present paper are twofold. The first contribution shows that the computations used in the outer estimation are inappropriate for reflective blocks. The second contribution involves introducing an alternative algorithm to overcome this drawback by using a new strategy based on considering the true structure of reflective blocks. Numerical studies and empirical simulations are provided to illustrate the advantages of the proposed algorithm compared to the classical one.
View
Exploring the structure of college students' adaptability by using cross‐lagged path analysis: The role of emotional adaptability
Article
Full-text available
  • Dec 2023
Adaptability is an important psychological trait for college students. However, the components of adaptability contained significant inconsistencies in previous studies. On the one hand, there were discrepancies among the adaptability dimensions. On the other hand, significant inconsistencies were found in the connections among different aspects of adaptability. Therefore, the current research aimed to investigate the latent relationship among various components of adaptability. To achieve this, 565 volunteers were recruited to complete a 5‐min cross‐sectional survey. Subsequently, 402 participants were recruited to complete an 8‐min longitudinal survey. The current study comprised two sub‐studies: Study 1 utilized a structural equation model to examine the relationship between various dimensions of adaptability in a cross‐sectional dataset, while Study 2 employed the cross‐lagged panel model to validate the latent relationship between emotional adaptability and other types of adaptability using a longitudinal dataset. Results from the cross‐sectional study indicated significant associations between emotional adaptability and other types of adaptability, with coefficients ranging from .231 to .588. The longitudinal study revealed that emotional adaptability at Time 2 and 3 could be predicted by learning adaptability, professional adaptability, and economic adaptability at Time 1 and 2. Consequently, the research concluded that individuals' emotional maladjustment could be predicted by maladaptive difficulties in learning, professional settings, homesickness, interpersonal relationships, and economics.
View
Financial Variables and Their Effects on The Development of Bank Credit and Productive Sectors in Iraq Using a Path Analysis Model
Article
Full-text available
  • Dec 2023
This study aims to measure and analyze the direct and indirect effects of the financial variables, namely (public spending, public revenues, internal debt, and external debt), on the non-oil productive sectors with and without bank credit as an intermediate variable, using quarterly data for the period (2004Q1–2021Q4), converted using Eviews 12. To measure the objective of the study, the path analysis method was used using IBM SPSS-AMOS. The study concluded that the direct and indirect effects of financial variables have a weak role in directing bank credit towards the productive sectors in Iraq, which amounted to (0.18), as a result of market risks or unstable expectations in the economy. In addition to the weak credit ratings of borrowers, this is on the one hand, and on the other hand, the majority of the credit granted by the Iraqi banking system has been directed towards the construction sector as a result of the guarantees that this sector can provide compared to other productive sectors. On the other hand, financial variables were not supportive in directing bank credit towards the development of these sectors in the country's GDP because the results reflected by the direct and indirect effects of financial variables were weak in supporting productive sectors with or without bank credit. (Especially since the local debt was competing with the private sector in obtaining bank credit, and this is called the effect of crowding out.)
View
Decrypting the Relationship Between Corruption and Human Development: Evidence from Indonesia
Article
Full-text available
  • Jun 2023
Corruption is considered endemic in a large part of the world's population and is believed to be a factor that disrupts market behavior and distorts competition, thereby hindering economic growth and human development. This study aims to unveil the impact of corruption on Indonesia's human development through various approaches, utilizing Fully-Modified Ordinary Least Squares (FMOLS), Dynamic Ordinary Least Squares (DOLS), Moderated Regression Analysis (MRA), Path Analysis, and Vector Error Correction Model (VECM) methods, with data covering the period from 1995 to 2022. The results of the estimation are discussed in three parts: 1) Dynamic Impact, by analyzing the long-term direct effect of corruption on human development; 2) Indirect Impact, by examining the role of government expenditure, tax revenue, and public debt in mediating the effect of corruption on human development; and 3) Causal Impact, by determining the unidirectional and bidirectional relationships between all variables studied. The findings indicate that corruption does not have a lasting direct impact on human development. Moreover, government expenditure and public debt play a role in moderating the impact of corruption on human development. Additionally, there is no causal link between corruption and human development, whereas there are causal connections between human development, government expenditure, tax revenue, and public debt. The results of this study will be valuable in assessing the extent of corruption's impact on human development, particularly in Indonesia, and aim to raise awareness of policymakers, hence encouraging individuals to participate in combating corruption.
View
New lights on the correlation matrix implied by a recursive path model
Article
Full-text available
Path Analysis is a statistical method to study the causal relationships between observed variables. The specification and the estimation steps are crucial in the whole process. In fact, the relationships between variables and their status are specified. In addition, the model parameters are estimated based on the so-called correlation matrix implied by the model. Two methods are available to compute this matrix: Jöreskog’s method and the Finite Iterative Method. Many researchers recommend that the variances of the endogenous variables to be fixed. For instance, diagonal elements are equal to 1. As a consequence, the present paper aims to show that the two methods are identical. Furthermore, numerical studies and empirical simulations illustrating the advantages of this recommendation are also given.
View
Acceptance of Artificial Intelligence Application in the Post-Covid Era and Its Impact on Faculty Members’ Occupational Well-being and Teaching Self Efficacy: A Path Analysis Using the UTAUT 2 Model
Article
Full-text available
  • Feb 2023
The purpose of the present study was to assess acceptance of Artificial Intelligence Application in the Post-covid Era and its impact of faculty members’ occupational well-being and teaching self efficacy using The UTAUT 2 Model. This study used a quantitative, non-experimental survey design to answer the research questions and study the relationships between the independent variables of performance expectancy, effort expectancy, social faculty members’ occupational well-being and teaching self efficacy. Faculty members from Umm AL-Qura University were targeted. An online questionnaire was used to collect data via Facebook and WhatsApp groups. I received a total of 350 questionnaire responses. They were 200 males(57.1%), and 150 females(42.9%). In confirmation of the research results, there is a significant positive relationship (p < .001) between occupational well-being (OWB)and teaching self efficacy(TSE) and performance expectancy (PE), effort expectancy (EE), social influence (SI), facilitating conditions (FC), price value (PV), and habit (HB), indicating that faculty members are influenced by the constructs established in the UTAUT2 model in the adoption of AI.
View
Realizing direct and indirect impact of environmental regulations on pollution: A path analysis approach to explore the mediating role of green innovation in G7 economies
Article
Full-text available
  • Jan 2023
  • ENVIRON SCI POLLUT R
The alarming impact of climate change and environmental pollutants has increased the focus of policymakers and think tanks’ focus on formulating environmental regulations. Environmental regulations may reduce emissions directly and indirectly, as postulated by the famous Porter Hypothesis. It shows that environmental regulation may enhance pollution-reducing innovation by reducing agency costs while at the same time increasing firms’ private benefit. The study is designed to investigate environmental regulations’ direct and indirect impact on CO2 and GHG emissions using innovations as mediation factors. The study employs a structural equation method using data on G7 economies from 1990 to 2020 to test the relationship between regulations, innovations, and pollution. The study findings confirm that environmental regulations help reduce emissions directly. Our findings also confirm the Porter hypothesis whereby regulations encourage innovations and result in reduced emissions through this indirect channel. The study findings have significant implications for controlling pollution through placing environmental regulations and encouraging innovations.
View
Generalizing the properties of the Finite Iterative Method for the Computation of the Covariance Matrix Implied by a Recursive Path Model
Article
Full-text available
  • Sep 2022
This paper generalizes the properties of the correlation matrix implied by a recursive path analysis model obtained using the Finite Iterative Method into the covariance case, where variables are no longer supposed to be standardized. We show that the implied covariance matrix computed using the Finite Iterative Method is affine with respect to each parameter of the considered model. Moreover, several other properties derive from this affinity and will be used to simplify the computation of the first as well as the second derivatives of the fit function used in the estimation of the model's parameters. Finally, we illustrate the advantages of the proposed properties compared to the classical approximation used to compute the aforementioned derivatives through numerical example.
View
View
The associations between attachment, self-esteem, fear of missing out, daily time expenditure, and problematic social media use: A path analysis model
Article
  • Feb 2023
  • ADDICT BEHAV
The present study investigated the factors that may be associated with a dysfunctional use of social media use, by exploring the association between adult attachment patterns and problematic social media use and analyzing the sequential mediation of self-esteem, fear of missing out (FoMO), and time spent on social media. A sample of 470 social media users (Mage = 33.76 years; SD = 14.267; 70 % women) completed the Bergen Social Media Addiction Scale, Fear of Missing Out Scale, Rosenberg Self-Esteem Scale, and Relationship Questionnaire. Results showed a path analysis model providing an excellent fit to the data (χ2 = 2.939, p = 0.230; GFI = 0.998, TLI = 0.987, CFI = 0.998, RMSEA = 0.032, SRMR = 0.016). A significant and positive total effect in the associations between preoccupied and fearful attachment patterns and problematic social media use emerged. Both preoccupied and fearful attachment patterns were also related to self-esteem, FoMO, and time spent on social media, which were sequentially associated and were, in turn, significantly related to problematic social media use. Finally, when self-esteem, FoMO, and time spent on social media were added into the model, they totally mediated the relationships between preoccupied and fearful attachment patterns and problematic social media use, suggesting a full multiple mediation model (R2 = 0.33). Such data may provide useful information for clinical practice to develop tailored interventions and prevention programs to address the compensatory and problematic use of social media.
View
Path analysis and mediating effects of influencing factors of land use carbon emissions in Chang-Zhu-Tan urban agglomeration
Article
  • Mar 2023
  • TECHNOL FORECAST SOC
Land use carbon emission is one of the main sources of greenhouse gases. In order to achieve carbon reduction, it is crucial to clarify the pathways of land use carbon emission influencing factors. The article takes Chang-Zhu-Tan urban agglomeration as the study area, combines the land use remote sensing data and energy consumption statistics from 1995 to 2018, and uses the STIRPAT extended model to identify the economic, population, energy, technology, policy, land and opening-up level as the latent variables affecting the land use carbon emission in the study area, to establish PLS-SEM to explore the influence of latent variables on dependent variables and the interaction between latent variables. The results show that the seven selected latent variables had good explanatory power on land use carbon emission with R² reaching 0.983. Economy, population, energy and land — the latent variables in this study — can directly influence land use carbon emission. This study found that land was the most important factor in increasing land use carbon emissions, with a path coefficient of 1.471, while economy played a negative role, with a path coefficient of −1.401. Latent variables other than energy and land all had mediating effects on the dependent variable or the remaining latent variables directly or indirectly. Indirect effects included complete mediation and partial mediation. For example, technology and opening-up level cannot directly influence the dependent variable, but can have a completely indirect effect by affecting energy (complete mediation). The fitness and superiority of the model developed in this paper were extremely high, with values of 0.067 and 0.846 for SRMR and GOF, respectively. This study helps to clarify the influence paths of land use carbon emission and figuratively depicts the path direction and degree of influence among influencing factors, which will help Chang-Zhu-Tan urban agglomeration achieve carbon emission reduction.
View