#
Smart Cities and Awareness of Sustainable Communities Related to Demand Response Programs: Data Processing with First-Order and Hierarchical Confirmatory Factor Analyses^{ †}

^{1}

^{2}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

- the creation of two measurement models (first-order CFA) that test the structure of factors that are behind the observed variables of the two large and complex questionnaires;
- the creation of several hierarchical CFA models, such as second-order and bi-factor models to reflect the relation between the items of the questionnaires and the awareness of electricity consumers;
- the testing of the models to prove that they do not capitalize on chance characteristics of the data, proving that the data-model fit is not random, and the model can generalize on different data sets;
- drawing interesting conclusions and providing information on the relationship between respondents’ answers and their awareness of environmental issues and implementation of DR programs.

## 2. Review of the Literature

## 3. Research Methodology

## 4. EDA of Input Data

## 5. Results

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Scatter plot and distribution of variables (

**a**) q1–q5, (

**b**) q3–q7 of the pre-trial data set.

**Figure 3.**Scatter plot and distribution of variables (

**a**) q1–q5, (

**b**) q6–q9 of the post-trial data set.

**Figure 8.**Path diagrams for the data set of the pre-trial questionnaire (

**a**) initial (

**b**) after modification.

**Figure 9.**Path diagrams for the post-trial questionnaire data set (

**a**) initial (

**b**) after modification.

data preq7factor; | variance |

infile ‘/home/simonaoprea0/preq7factor.csv’ dsd; | e1-e7 = vare1-vare7, |

input id $ q1-q7; | F1 = 1, F2 = 1; |

run; | cov |

proc calis modification residual robust; | F1 F2 = covF1F2; |

lineqs | var q1-q7; |

q1 = p1 F1 + e1, | pathdiagram diagram = standard |

q2 = p2 F2 + e2, | scale = 0.75 EXOGCOVARIANCE |

q3 = p3 F2 + e3, | label = [F1 = “Social_economic” |

q4 = p4 F1 + e4, | F2 = “Behavioural”] |

q5 = p5 F2 + e5, | dh = 1000 dw = 1000 |

q6 = p6 F1 + e6, | textsizemin = 10; |

q7 = p7 F1 + e7; | run; |

data post9factor; | q9 = p9 F2 + e9; |

infile ‘/home/simonaoprea0/post9factor.csv’ dsd; | variance |

input id $ q1 q2 q3 q4 q5 q6 q7 q8 q9; | e1−e9 = vare1−vare9, |

run; | F1 = 1, F2 = 1; |

proc calis modification residual robust; | cov |

lineqs | F1 F2 = covF1F2; |

q1 = p1 F2 + e1, | var q1−q9; |

q2 = p2 F1 + e2, | pathdiagram diagram = standard scale = 0.75 EXOGCOVARIANCE |

q3 = p3 F2 + e3, | label = [F1 = “Social_economic” F2 = “Behavioural”] dh = 1000 dw = 1000 textsizemin = 10; |

q4 = p4 F2 + e4, | run; |

q5 = p5 F1 + e5, | - |

q6 = p6 F1 + e6, | - |

q7 = p7 F2 + e7, | - |

q8 = p8 F2 + e8, | - |

Modelling Information for Pre-Trial Questionnaire | Modelling Information for Post-Trial Questionnaire | ||
---|---|---|---|

Modeling Information | Modeling Information | ||

Robust Maximum Likelihood Estimation | Robust Maximum Likelihood Estimation | ||

Data Set | WORK.PREQ7FACTOR | Data Set | WORK.POST9FACTOR |

N Records Read | 4232 | N Records Read | 3423 |

N Records Used | 4232 | N Records Used | 3423 |

N Obs | 4232 | N Obs | 3423 |

Model Type | LINEQS | Model Type | LINEQS |

Analysis | Means and Covariances | Analysis | Means and Covariances |

Variables for the Pre-Trial Questionnaire | Variables for the Post-Trial Questionnaire | ||||
---|---|---|---|---|---|

Variables in the Model | Variables in the Model | ||||

Number of Endogenous Variables = 7 | Number of Endogenous Variables = 9 | ||||

Number of Exogenous Variables = 9 | Number of Exogenous Variables = 11 | ||||

Endogenous | Manifest | q1 q2 q3 q4 q5 q6 q7 | Endogenous | Manifest | q1 q2 q3 q4 q5 q6 q7 q8 q9 |

Latent | - | Latent | |||

Exogenous | Manifest | - | Exogenous | Manifest | |

- | Latent | F1 F2 | - | Latent | F1 F2 |

- | Error | e1 e2 e3 e4 e5 e6 e7 | - | Error | e1 e2 e3 e4 e5 e6 e7 e8 e9 |

Simple Statistics for the Pre-Trial Questionnaire | Simple Statistics for the Post-Trial Questionnaire | ||||
---|---|---|---|---|---|

Simple Statistics | Simple Statistics | ||||

Variable | Mean | Std Dev | Variable | Mean | Std Dev |

q1 | 45.91966 | 6.49056 | q1 | 8.53754 | 3.22219 |

q2 | 16.78474 | 3.06561 | q2 | 20.61846 | 7.10923 |

q3 | 23.94849 | 6.01536 | q3 | 16.0894 | 5.63135 |

q4 | 13.99669 | 2.05743 | q4 | 25.89833 | 5.57182 |

q5 | 15.60562 | 3.16985 | q5 | 23.71458 | 3.84094 |

q6 | 18.40052 | 4.01145 | q6 | 3.43003 | 4.67816 |

q7 | 50.69565 | 11.09745 | q7 | 70.04061 | 41.94054 |

- | q8 | 17.14607 | 19.24341 | ||

- | q9 | 52.78761 | 42.62345 |

Iteration | Restarts | Function Calls | Active Constraints | Objective Function | Objective Function Change | Max Abs Gradient Element | Lambda | Ratio between Actual and Predicted Change |
---|---|---|---|---|---|---|---|---|

1 | 0 | 4 | 0 | 0.01052 | 0.00650 | 0.00488 | 0 | 0.936 |

2 | 0 | 7 | 0 | 0.00975 | 0.000769 | 0.00411 | 0.0105 | 0.883 |

3 | 0 | 10 | 0 | 0.00937 | 0.000377 | 0.00415 | 0.00506 | 0.926 |

4 | 0 | 13 | 0 | 0.00919 | 0.000181 | 0.00281 | 0.00334 | 0.940 |

5 | 0 | 16 | 0 | 0.00910 | 0.000089 | 0.00248 | 0.00197 | 0.918 |

6 | 0 | 19 | 0 | 0.00906 | 0.000046 | 0.00170 | 0.00133 | 0.946 |

7 | 0 | 22 | 0 | 0.00903 | 0.000022 | 0.000901 | 0.00111 | 0.983 |

8 | 0 | 24 | 0 | 0.00903 | 5.733 × 10^{−6} | 0.00379 | 0.00008 | 0.338 |

9 | 0 | 26 | 0 | 0.00901 | 0.000015 | 0.000491 | 0 | 1.041 |

10 | 0 | 28 | 0 | 0.00901 | 5.027 × 10^{−7} | 0.000056 | 0 | 1.173 |

11 | 0 | 30 | 0 | 0.00901 | 3.296 × 10^{−8} | 0.000031 | 0 | 1.270 |

12 | 0 | 32 | 0 | 0.00901 | 2.903 × 10^{−9} | 7.566 × 10^{−6} | 0 | 1.290 |

Iteration | Restarts | Function Calls | Active Constraints | Objective Function | Objective Function Change | Max Abs Gradient Element | Lambda | Ratio between Actual and Predicted Change |
---|---|---|---|---|---|---|---|---|

1 | 0 | 4 | 0 | 0.15703 | 0.0224 | 0.0292 | 0 | 1.159 |

2 | 0 | 6 | 0 | 0.15603 | 0.000998 | 0.00164 | 0 | 1.148 |

3 | 0 | 8 | 0 | 0.15599 | 0.000043 | 0.00103 | 0 | 1.129 |

4 | 0 | 10 | 0 | 0.15599 | 2.589 × 10^{−6} | 0.000035 | 0 | 1.072 |

5 | 0 | 12 | 0 | 0.15599 | 1.681 × 10^{−7} | 0.000077 | 0 | 0.991 |

6 | 0 | 14 | 0 | 0.15599 | 1.187 × 10^{−8} | 9.588 × 10^{−6} | 0 | 0.905 |

Standardized Effects in Linear Equations for Pre-Trial Questionnaire | ||||||
---|---|---|---|---|---|---|

Variable | Predictor | Parameter | Estimate | Standard Error | t Value | Pr > |t| |

q1 | F1 | p1 | 0.40652 | 0.03209 | 12.6685 | <0.0001 |

q2 | F2 | p2 | 2.97743 | 0.02871 | 103.7 | <0.0001 |

q3 | F2 | p3 | −0.06694 | 0.00504 | −13.2872 | <0.0001 |

q4 | F1 | p4 | 0.03290 | 0.01791 | 1.8370 | 0.0662 |

q5 | F2 | p5 | 0.03640 | 0.00503 | 7.2344 | <0.0001 |

q6 | F1 | p6 | 0.19495 | 0.02102 | 9.2762 | <0.0001 |

q7 | F1 | p7 | 0.85228 | 0.06165 | 13.8250 | <0.0001 |

Standardized Effects in Linear Equations for Post-Trial Questionnaire | ||||||
---|---|---|---|---|---|---|

Variable | Predictor | Parameter | Estimate | Standard Error | t Value | Pr > |t| |

q1 | F2 | p1 | 0.42884 | 0.01515 | 28.3030 | <0.0001 |

q2 | F1 | p2 | 0.01971 | 0.01529 | 1.2890 | 0.1974 |

q3 | F2 | p3 | −0.21572 | 0.01739 | −12.4069 | <0.0001 |

q4 | F2 | p4 | 0.09304 | 0.01801 | 5.1659 | <0.0001 |

q5 | F1 | p5 | −0.50338 | 0.03143 | −16.0161 | <0.0001 |

q6 | F1 | p6 | −0.23909 | 0.02111 | −11.3272 | <0.0001 |

q7 | F2 | p7 | 0.91882 | 0.00804 | 114.3 | <0.0001 |

q8 | F2 | p8 | 0.24149 | 0.01719 | 14.0458 | <0.0001 |

q9 | F2 | p9 | 0.76306 | 0.00965 | 79.1111 | <0.0001 |

Wald Test for Pre-Trial Questionnaire | Wald Test for Post-Trial Questionnaire | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

Stepwise Multivariate Wald Test | Stepwise Multivariate Wald Test | ||||||||||

Parm | Cumulative Statistics | Univariate Increment | Parm | Cumulative Statistics | Univariate Increment | ||||||

Chi-Square | DF | Pr > ChiSq | Chi-Square | Pr > ChiSq | Chi-Square | DF | Pr > ChiSq | Chi-Square | Pr > ChiSq | ||

p4 | 3.3704 | 1 | 0.0664 | 3.3704 | 0.0664 | p2 | 1.6603 | 1 | 0.1976 | 1.6603 | 0.1976 |

Index Category | Performance Indicator | PRE | PREq4 | POST | POSTq2 |
---|---|---|---|---|---|

Absolute Index | Fit Function | 0.0162 | 0.0077 | 0.1418 | 0.1379 |

- | Chi-Square | 68.74 | 32.53 | 485.33 | 471.88 |

Chi-Square DF | 13 | 8 | 26 | 19 | |

Pr > Chi-Square | <0.0001 | <0.0001 | <0.0001 | <0.0001 | |

Z-Test of Wilson and Hilferty | 5.8077 | 3.7435 | 17.9693 | 17.8397 | |

Hoelter Critical N | 1377 | 2017 | 275 | 219 | |

Root Mean Square Residual (RMR) | 0.4779 | 0.5003 | 8.2502 | 9.0782 | |

Standardized RMR (SRMR) | 0.0241 | 0.0189 | 0.0443 | 0.0486 | |

Goodness of Fit Index (GFI) | 0.9955 | 0.9974 | 0.9701 | 0.9674 | |

Parsimony Index | Adjusted GFI (AGFI) | 0.9902 | 0.9933 | 0.9482 | 0.9382 |

- | Parsimonious GFI | 0.6162 | 0.5320 | 0.7006 | 0.6564 |

RMSEA Estimate | 0.0318 | 0.0269 | 0.0719 | 0.0835 | |

RMSEA Lower 90% Confidence Limit | 0.0247 | 0.0177 | 0.0663 | 0.0770 | |

RMSEA Upper 90% Confidence Limit | 0.0394 | 0.0369 | 0.0775 | 0.0901 | |

Probability of Close Fit | 1.0000 | 1.0000 | <0.0001 | <0.0001 | |

ECVI Estimate | 0.0234 | 0.0138 | 0.1530 | 0.1479 | |

ECVI Lower 90% Confidence Limit | 0.0181 | 0.0105 | 0.1331 | 0.1282 | |

ECVI Upper 90% Confidence Limit | 0.0304 | 0.0189 | 0.1750 | 0.1697 | |

Akaike Information Criterion | 98.74 | 58.53 | 523.33 | 505.88 | |

Bozdogan CAIC | 209.00 | 154.08 | 658.96 | 627.23 | |

Schwarz Bayesian Criterion | 194.00 | 141.08 | 639.96 | 610.23 | |

McDonald Centrality | 0.9934 | 0.9971 | 0.9351 | 0.9360 | |

Incremental Index | Bentler Comparative Fit Index | 0.9440 | 0.9744 | 0.9125 | 0.9141 |

- | Bentler-Bonett NFI | 0.9323 | 0.9665 | 0.9082 | 0.9110 |

Bentler-Bonett Non-normed Index | 0.9095 | 0.9519 | 0.8788 | 0.8734 | |

Bollen Normed Index Rho1 | 0.8907 | 0.9372 | 0.8728 | 0.8688 | |

Bollen Non-normed Index Delta2 | 0.9444 | 0.9745 | 0.9127 | 0.9142 | |

James et al. Parsimonious NFI | 0.5772 | 0.5155 | 0.6559 | 0.6182 |

- | - | Complete Data Set | 1st Subset | 2nd Subset | 3rd Subset | 4th Subset |
---|---|---|---|---|---|---|

Absolute Index | Fit Function | 0.0077 | 0.0219 | 0.0131 | 0.0071 | 0.0109 |

- | Chi-Square | 32.53 | 23.1501 | 13.8552 | 7.5028 | 11.4965 |

Chi-Square DF | 8 | 8 | 8 | 8 | 8 | |

Pr > Chi-Square | <0.0001 | 0.0032 | 0.0856 | 0.4835 | 0.1751 | |

Z-Test of Wilson and Hilferty | 3.7435 | 2.7168 | 1.3721 | 0.0397 | 0.9375 | |

Hoelter Critical N | 2017 | 709 | 1184 | 2185 | 1426 | |

Root Mean Square Residual (RMR) | 0.5003 | 0.6682 | 0.5539 | 0.4711 | 0.7003 | |

Standardized RMR (SRMR) | 0.0189 | 0.0296 | 0.0239 | 0.0166 | 0.0226 | |

Goodness of Fit Index (GFI) | 0.9974 | 0.9927 | 0.9956 | 0.9976 | 0.9965 | |

Parsimony Index | Adjusted GFI (AGFI) | 0.9933 | 0.9808 | 0.9884 | 0.9938 | 0.9907 |

- | Parsimonious GFI | 0.5320 | 0.5294 | 0.5310 | 0.5321 | 0.5314 |

RMSEA Estimate | 0.0269 | 0.0423 | 0.0263 | 0.0000 | 0.0203 | |

RMSEA Lower 90% Confidence Limit | 0.0177 | 0.0228 | 0.0000 | 0.0000 | 0.0000 | |

RMSEA Upper 90% Confidence Limit | 0.0369 | 0.0630 | 0.0490 | 0.0346 | 0.0444 | |

Probability of Close Fit | 1.0000 | 0.7037 | 0.9580 | 0.9978 | 0.9822 | |

ECVI Estimate | 0.0138 | 0.0467 | 0.0379 | 0.0319 | 0.0356 | |

ECVI Lower 90% Confidence Limit | 0.0105 | 0.0365 | 0.0324 | 0.0324 | 0.0324 | |

ECVI Upper 90% Confidence Limit | 0.0189 | 0.0641 | 0.0516 | 0.0419 | 0.0482 | |

Akaike Information Criterion | 58.53 | 49.1501 | 39.8552 | 33.5028 | 37.4965 | |

Bozdogan CAIC | 154.08 | 126.6839 | 117.3890 | 111.0365 | 115.0303 | |

Schwarz Bayesian Criterion | 141.08 | 113.6839 | 104.3890 | 98.0365 | 102.0303 | |

McDonald Centrality | 0.9971 | 0.9929 | 0.9972 | 1.0002 | 0.9983 | |

Incremental Index | Bentler Comparative Fit Index | 0.9744 | 0.9433 | 0.9754 | 1.0000 | 0.9870 |

- | Bentler-Bonett NFI | 0.9665 | 0.9180 | 0.9452 | 0.9711 | 0.9596 |

Bentler-Bonett Non-normed Index | 0.9519 | 0.8938 | 0.9539 | 1.0038 | 0.9757 | |

Bollen Normed Index Rho1 | 0.9372 | 0.8463 | 0.8973 | 0.9459 | 0.9242 | |

Bollen Non-normed Index Delta2 | 0.9745 | 0.9448 | 0.9761 | 1.0020 | 0.9873 | |

James et al. Parsimonious NFI | 0.5155 | 0.4896 | 0.5041 | 0.5179 | 0.5118 |

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**MDPI and ACS Style**

Oprea, S.-V.; Bâra, A.; Ciurea, C.-E.; Stoica, L.F. Smart Cities and Awareness of Sustainable Communities Related to Demand Response Programs: Data Processing with First-Order and Hierarchical Confirmatory Factor Analyses. *Electronics* **2022**, *11*, 1157.
https://doi.org/10.3390/electronics11071157

**AMA Style**

Oprea S-V, Bâra A, Ciurea C-E, Stoica LF. Smart Cities and Awareness of Sustainable Communities Related to Demand Response Programs: Data Processing with First-Order and Hierarchical Confirmatory Factor Analyses. *Electronics*. 2022; 11(7):1157.
https://doi.org/10.3390/electronics11071157

**Chicago/Turabian Style**

Oprea, Simona-Vasilica, Adela Bâra, Cristian-Eugen Ciurea, and Laura Florentina Stoica. 2022. "Smart Cities and Awareness of Sustainable Communities Related to Demand Response Programs: Data Processing with First-Order and Hierarchical Confirmatory Factor Analyses" *Electronics* 11, no. 7: 1157.
https://doi.org/10.3390/electronics11071157