# Connecting Climate and Communicable Disease to Penta Helix Using Hierarchical Likelihood Structural Equation Modelling

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## Abstract

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## 1. Introduction

## 2. Hierarchical Structural Equation Models (HSEMs)

- Inadmissible solution: This happens because variance-based SEMs are not covariance so that the singular matrix problem will never occur.
- Factor indeterminacy: Factor indeterminacy is a condition that causes latent variable scores that cannot be obtained. The sample size in traditional SEMs can be estimated as ten times the number of formative indicators (ignoring reflective indicators) [52,53,54]. Ten times the amounts of structural paths in the inner model and small sample sizes 30–50 or large samples over 200. In determining the sample size, the HSEM approach states that the strength of the analysis is based on the portion of the model that has the most considerable number of predictors. Minimum recommended ranges are from 30 to 100 cases. HSEMs consist of external relationships (outer models or measurement models) and internal relationships (inner models or structural models) [54]. The relationship is defined as two linear equations, namely the measurement model that unites the relationship of the latent variable with a group of explanatory variables and the structural model that is the relationship among the latent variables [51,52,55].

#### 2.1. Inner Model

- $i:$ The number of paths from the free latent variable to the non-free latent variable
- $j:$ The number of latent variables
- ${\eta}_{j}:$ Latent variable j-th
- ${\eta}_{i}:$ Latent variable i-th
- ${\beta}_{ji}:$ Coefficient path of the i-th exogenous latent variable to the j-th endogenous latent variable
- ${\gamma}_{ji}:$ Coefficient of the i-th endogenous latent variable to the j-th endogenous latent variable
- ${\beta}_{0j}$: Intercept
- ${\zeta}_{i}:$ Inner residual

#### 2.2. Outer Model

#### 2.3. Reflective Relations

#### 2.4. Formative Relations

## 3. Datasets and Results

#### 3.1. Synergy of Penta-Helix in Health Issues

#### 3.2. Communicable Disease

#### 3.3. Communicable Disease against Climate

#### 3.4. Model Construction

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Appendix A

**Step 0**: Outer Weight Initialization. At this stage, an initialization is made, which is to determine any arbitrary value for outer weight. To make it easier, the weights of all indicators are the same: ${w}_{jk}$. Indicators are scaled to have unit variance (mean = 0, variance = 1).**Step 1**: Outside Approximation. After the outer weight is estimated, the estimation of the measurement model is then performed, which illustrates that the latent variable is the sum of the multiplication of weights with indicators.**Step 2**: Determination of Inner Weight. The initial value of the latent variable has been obtained; then, recalculate the latent variable differently. The latent variable is considered a linear combination of other related latent variables.**Step 3**: Structural Model Estimation (Inside Approximation). After the inner weight is obtained, then estimation is made of the structural model.**Step 4**: Updating the Weight of the Measurement Model or Updating Outer Weight. The process of updating the weight of the measurement model is divided into two; first, for reflective indicators (mode A) and, second, formative (mode B).

**mode A**:

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Latent Variable | Dillon–Goldstein’s rho |
---|---|

Climate | 0.640 |

Social | 0.864 |

Food Water Borne | 0.957 |

Airborne or Droplet | 0.975 |

Vector Borne | 0.886 |

Sexually Transmitted or Blood Borne | 0.977 |

Contact Transmission | 0.862 |

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**MDPI and ACS Style**

Caraka, R.E.; Noh, M.; Chen, R.-C.; Lee, Y.; Gio, P.U.; Pardamean, B. Connecting Climate and Communicable Disease to Penta Helix Using Hierarchical Likelihood Structural Equation Modelling. *Symmetry* **2021**, *13*, 657.
https://doi.org/10.3390/sym13040657

**AMA Style**

Caraka RE, Noh M, Chen R-C, Lee Y, Gio PU, Pardamean B. Connecting Climate and Communicable Disease to Penta Helix Using Hierarchical Likelihood Structural Equation Modelling. *Symmetry*. 2021; 13(4):657.
https://doi.org/10.3390/sym13040657

**Chicago/Turabian Style**

Caraka, Rezzy Eko, Maengseok Noh, Rung-Ching Chen, Youngjo Lee, Prana Ugiana Gio, and Bens Pardamean. 2021. "Connecting Climate and Communicable Disease to Penta Helix Using Hierarchical Likelihood Structural Equation Modelling" *Symmetry* 13, no. 4: 657.
https://doi.org/10.3390/sym13040657