The effect of latent and error non-normality on corrections to the test statistic in structural equation modeling

In structural equation modeling, several corrections to the likelihood-ratio model test statistic have been developed to counter the effects of non-normal data. Previous robustness studies investigating the performance of these corrections typically induced non-normality in the indicator variables. However, non-normality in the indicators can originate from non-normal errors or non-normal latent factors. We conducted a Monte Carlo simulation to analyze the effect of non-normality in factors and errors on six different test statistics based on maximum likelihood estimation by evaluating the effect on empirical rejection rates and derived indices (RMSEA and CFI) for different degrees of non-normality and sample sizes. We considered the uncorrected likelihood-ratio model test statistic and the Satorra–Bentler scaled test statistic with Bartlett correction, as well as the mean and variance adjusted test statistic, a scale-shifted approach, a third moment-adjusted test statistic, and an approach drawing inferences from the relevant asymptotic chi-square mixture distribution. The results indicate that the values of the uncorrected test statistic—compared to values under normality—are associated with a severely inflated type I error rate when latent variables are non-normal, but virtually no differences occur when errors are non-normal. Although no general pattern regarding the source of non-normality for all analyzed measures of fit can be derived, the Satorra–Bentler scaled test statistic with Bartlett correction performed satisfactorily across conditions.

Research on the similarity of vibration characteristics of naval gun bracket based on similarity theory

The similar scale model experiment can provide some reference for the research and development of naval gun weapons. This paper takes the naval gun bracket as an example to explain. Based on the dimensional analysis, equation analysis and finite element method, the modal parameter similarity relationship between the original model for bracket and the shrinkage ratio model is established. The results show that the error of predicting the natural frequency of the original model based on similarity relation is less than 2% comparing with the results of finite element numerical simulation, and the error is less than 10% comparing with the experimental results, and the mode of shrinkage model is close to that of the original model. It is proved that the theoretical method in this paper is feasible and practical in engineering. Therefore, the vibration characteristics of the original model can be estimated by analyzing the vibration characteristics of the carrier shrinkage ratio model, which provides a reference for ship gun designers.

Integrating Landslide Typology with Weighted Frequency Ratio Model for Landslide Susceptibility Mapping: A Case Study from Lanzhou City of Northwestern China

Although numerous models have been employed to address the issue of landslide susceptibility at regional scale, few have incorporated landslide typology into a model application. Thus, the aim of the present study is to perform landslide susceptibility zonation taking landslide classification into account using a data-driven model. The specific objective is to answer the question: how to select reasonable influencing factors for different types of landslides so that the accuracy of susceptibility assessment can be improved? The Qilihe District in Lanzhou City of northwestern China was undertaken as the test area, and a total of 12 influencing factors were set as the predictive variables. An inventory map containing 227 landslides was created first, which was divided into shallow landslides and debris flows based on the geological features, distribution, and formation mechanisms. A weighted frequency ratio model was proposed to calculate the landslide susceptibility. The weights of influencing factors were calculated by the integrated model of logistic regression and fuzzy analytical hierarchy process, whereas the rating among the classes within each factor was obtained by a frequency ratio algorithm. The landslide susceptibility index of each cell was subsequently calculated in GIS environment to create landslide susceptibility maps of different types of landslide. The analysis and assessment process were separately performed for each type of landslide, and the final landslide susceptibility map for the entire region was produced by combining them. The results showed that 73.3% of landslide pixels were classified into “very high” or “high” susceptibility zones, while “very low” or “low” susceptibility zones covered only 3.6% of landslide pixels. The accuracy of the model represented by receiver operating characteristic curve was satisfactory, with a success rate of 70.4%. When the landslide typology was not considered, the accuracy of resulted maps decreased by 1.5~5.4%.

Minimum Void Ratio Model Established from Tailings and Determination of Optimal Void Ratio

Minimum void ratio of tailings and its value change with fine content and are key design parameters for tailing consolidation and seepage stability. Based on the distribution of tailing grains with the sedimentary beach, we establish a minimum void ratio model for tailing grain in binary size, which requires only two parameters ( ε and ω ). Calibrations of the model using 168 groups of tests (22 kinds of grain size ratios with 7-9 kinds of fine contents) show two parameters that are fitting for power function, and the exponent values increase with the dominant grain size expanded. Besides, the exponent values are related to the equivalent grain size ratio, dominant grain size, and shape characteristics. The minimum void ratios with fine content are predicted under the derived model. Good agreement was obtained between the predictions and measurements, and the average discrepancies are less than 10%. And optimal void ratio and optimal fine content can be predicted, and the values are in good agreement with the experimental ones. Furthermore, based on the predicted optimal void ratio, the exponential relationship between the optimal void ratio and the equivalent grain size ratio may have no influence on the derived dominant grain size and shape characteristics. For tailings, further work is needed to verify if the derived exponential relationship between the optimal void ratio and the equivalent grain size ratio is valid.