A Study of the Quantitative Influence of Intercultural Factors on Textual Coherence in English and American Literary Translation

Lexical features are divided into three categories: lexical diversity, word frequency information and lexical semantics.

Lexical diversity includes real word class symbol-to-symbol ratio V1, all word class symbol-to-symbol ratio V2, MTLD-based lexical diversity V3, and VOCD-based lexical diversity V4, which can reflect the richness of vocabulary in the text.

Word frequency information includes three indicators, real word word frequency V5 in CELEX database, logarithmic frequency of all words V6 in CELEX database and lowest logarithmic word frequency of real words V7 in CELEX database, which reflects the frequency of vocabulary usage in the text.

Lexical semantics includes real word familiarity V8, real word concreteness V9, real word imagery V10, real word polysemy V11, real word number of sense items V12, noun superordinate relation V13, verb superordinate relation V14, and noun and verb superordinate relation V15, with a total of 8 indicators.

Syntactic features are categorized into five categories: length of linguistic output, sentence complexity, number of subordinate structures, number of parallel structures, and number of phrase structures.

Linguistic output length includes average length of clauses S1, average length of sentences S2, and average length of T-units S3.

Sentence complexity is the number of clauses in a sentence S4.

Subordinate structure includes the number of clauses in T-units S5, the number of complex T-units in T-units S6, the number of dependent clauses in clauses S7, and the number of subordinate clauses in T-units S8.

Parallel structures include the number of parallel phrases in clauses S9, the number of parallel phrases in T-units S10, and the number of T-units in sentences S11.

Phrase structure includes the number of compound nouns in clauses S12, the number of compound nouns in T-units S13, and the number of verb phrases in T-units S14.

Articulation features are divided into three categories: referential articulation, latent semantic analysis, and conjunction.

Referential articulation includes adjacent noun overlap L1, adjacent argument element overlap L2, adjacent stem overlap L3, adjacent real word overlap L4, noun overlap L5, argument element overlap L6, stem overlap L7, and real word overlap L8.

Latent semantic analysis includes semantic similarity of neighboring sentences L9, semantic similarity of all sentences in a paragraph L10, semantic similarity of neighboring paragraphs L11, and the semantic similarity ratio of old and new information L12.

Conjunctions include various types of conjunctions L13, causal conjunctions L14, logical conjunctions L15, transitive/contrastive conjunctions L16, temporal conjunctions L17 and additional conjunctions L18.

The basic principle of modeling is to carefully analyze the problem and identify the various factors associated with it. Among the various influencing factors, the main factors will be taken into account, and the secondary factors that have little to do with the problem will be eliminated, in order to find a more reasonable mathematical model. A well-constructed model not only explains the problem’s nature, but also ensures that the model is not too complex that the real problem cannot be solved. Regression analysis is an effective tool commonly used in statistical analysis. The multivariate linear regression model for m independent variable is formulated as: 1y=β0+β1x1+β2x2+⋯+βmxm+ε$$y = {\beta _0} + {\beta _1}{x_1} + {\beta _2}{x_2} + \cdots + {\beta _m}{x_m} + \varepsilon $$

Where, y is the dependent variable. x₁, x₂,…,x_m is expressed as the independent variable that has a significant effect on the dependent variable y, and β₀, α₁,…,β_m is the regression coefficient corresponding to the respective variable. ε is the error variable representing the effect of random factors other than x₁, x₂,…,x_m on y. A good regression model requires that the variables x₁, x₂,…,x_m be independent of each other.

Stepwise regression, as a method of screening independent variables when constructing linear regression models, follows the basic principle of dynamically combining the two processes of introducing independent variables into the model and removing them from the model, with both in and out, and screening the independent variables in a dynamic way, so as to avoid the problem of covariance among the independent variables finally selected into the regression model to a large extent.

In determining whether a new variable is introduced or excluded in a regression equation, specific mathematical means are needed to determine whether the effect of this variable on the dependent variable is significant. The partial F test, on the other hand, provides an alternative for solving this problem. Before discussing the partial F-test, the method of significance testing performed on multiple linear regression equations, the F-test, is introduced.

In essence, testing the significance of a multiple linear regression equation is actually an overall assessment of whether independent variable x₁, x₂,…,x_m has a linear effect on dependent variable y. For this reason the original hypothesis is formulated: 2H0:β1=β2=⋯=βm=0$${H_0}:{\beta _1} = {\beta _2} = \cdots = {\beta _m} = 0$$

If H₀ is not rejected, it implies that the dependent variable is linearly independent of all independent variables. In order to test the original hypothesis H₀, it is necessary to build the F statistic from the sum-of-squares decomposition equation, which is used to judge the original hypothesis directly from the regression effect, as follows: 3∑i=1n(yi−y¯)2=∑i=1n(y^−y¯)2+∑i=1n(yi−y^i)2$$\sum\limits_{i = 1}^n {{{\left( {{y_i} - \bar y} \right)}^2}} = \sum\limits_{i = 1}^n {{{(\hat y - \bar y)}^2}} + \sum\limits_{i = 1}^n {{{\left( {{y_i} - {{\hat y}_i}} \right)}^2}} $$ where ∑n(yi−y¯)2$$\mathop \sum \limits^n {\left( {{y_i} - \bar y} \right)^2}$$ is called the total deviation sum of squares and is denoted as SST. ∑n(y^−y¯)2$$\mathop \sum \limits^n {\left( {\hat y - \bar y} \right)^2}$$ is called the regression sum of squares and is denoted as SSR. ∑i=1n(yi−y^i)2$$\sum\limits_{i = 1}^n {{{\left( {{y_i} - {{\hat y}_i}} \right)}^2}} $$ is called the residual sum of squares and is denoted as SSE.

Thus the sum of squares decomposition equation can be abbreviated as: 4SST=SSR+SSE$$SST = SSR + SSE$$

The Construct F test statistic is as follows: 5F=SSR/mSSE/(n−m−1)$$F = {{SSR/m} \over {SSE/\left( {n - m - 1} \right)}}$$

Accordingly, the original hypothesis H₀ can be judged from the magnitude of the value of the F statistic to test the significance of the regression equation. This is done as follows: for the data (i = 1,2,…,n) given in the particular problem, the regression sum of squares SSR and the residual sum of squares SSE are calculated, and then the value of F is obtained according to equation (5), and the corresponding critical value F_α is obtained by checking the distribution table of F from the predetermined significance level α (e.g., 0.05).

If F > F_α, hypothesis H₀ is rejected, indicating that the regression equation is significant. That is, the probability of making an error in accepting the conclusion that “the independent variable as a whole has a linear effect on the dependent variable y” is no more than α. If F≤ F_α the original hypothesis H₀ is accepted, indicating that the regression equation is not significant. The test can also be done on the basis of the value of significance p, and when the value of p is <α, the original hypothesis H₀ is rejected, and when the value of p is ≥ α, the original hypothesis H₀ is accepted.

In multiple linear regression, significance by the F test merely indicates that the dependent variable y has a significant linear relationship to the independent variables x₁, x₂,…, x_m as a whole, but it does not indicate that the dependent variable y has a significant regression effect on each of the independent variables x_j. Similarly, the regression coefficients for one or more of the independent variables x_j in the set of independent variables are not significant, but the F test for the overall significance of the regression equation may still be significant. Therefore, the discussion will switch to testing the significance of the independent variables x_j. A linear regression of the dependent variable y on the independent variables x₁, x₂,…, x_m and notated as a full model yields SSE and SSR Now, excluding one of the independent variables x_j from the set of independent variables yields a reduced model consisting of m–1 independent variables as follows: 6y=β0+β1x1+⋯+βj−1xj−1+βj+1xj+1+⋯+βmxm+ε$$y = {\beta _0} + {\beta _1}{x_1} + \cdots + {\beta _{j - 1}}{x_{j - 1}} + {\beta _{j + 1}}{x_{j + 1}} + \cdots + {\beta _m}{x_m} + \varepsilon $$

Noting that the residual sum of squares from the reduced model (6) is SSE_(j) and the regression sum of squares is SSR_(j), the contribution of independent variable x_j to the regression is ΔSSR_j) = SSR – SSR_(j), which is called the biased regression sum of squares of independent variable x_j. The partial F statistic is obtained: 7Fj=ΔSSR(j)/1SSE/(n−m−1)$${F_j} = {{\Delta SS{R_{\left( j \right)}}/1} \over {SSE/\left( {n - m - 1} \right)}}$$

In the subsequent discussion of the analysis, determining whether a new variable is introduced or excluded from the regression equation requires a partial F test using equation (7), which serves as the basis for variable screening.

The correlation analysis revealed that 30 indicators out of 47 linguistic feature indicators have a significant correlation with the textual consistency of the sample English and American literary translations. The relevant linguistic features of textual coherence of the translations are shown in Fig. 2. Due to the multicollinearity among the indicators, 20 indicators were retained as potential variables for predicting textual coherence of the translations after screening, and the correlations were between -0.4 and 0.3.

Figure 2.

The linguistic characteristics of text consistency of the translation

In order to further examine the extent to which these latent variables contribute to the translated scores, stepwise regression analyses were conducted, and Table 1 shows the results of the modeling of the consistency of the translated text. The 10 indicators, namely, all word class talismanic formant ratio V2, VOCD-based lexical diversity V4, real word frequency in CELEX database V5, real word familiarity V8, real word polysemy V11, the number of juxtaposed phrases in clauses S9, the number of verbal phrases in T-units S14, overlap of real words L8, semantic similarity of neighboring passages L11, and the ratio of the semantic similarity of the old and the new information L12, were able to explain the 58.74% of text consistency in English and American literary translations (R²=0.6648, adjusted R²=0.5874, p<0.001). Among them, the semantic similarity ratio of old and new information, L12, has the greatest effect on text consistency in English and American literary translations, with an estimated coefficient of 124.416, followed by real-word overlap, L8, and the ratio of all lexical categories of talismans to formulas, V2, both of which have a significant negative effect on text consistency.

Textual coherence in English and American literary translation is the explanatory variable of this study, and its measurement draws on the analysis of the model of textual coherence in English and American literary translation based on the prediction of linguistic features above. Intercultural factors in English and American literary translation are the explanatory variable of this study, and their measurement is carried out through a questionnaire survey. Taking professional English translators as the target, the questionnaire was prepared based on the sample English and American literature translation works and cross-cultural factors in each dimension, 124 questionnaires were returned, 108 valid questionnaires were obtained, and the validity rate of the questionnaire was 87.1%.

AMOS 20.0 was used to construct the structural equation model. Fit evaluation and path analysis were performed on the model, and the structural equation model was applied to perform multi-cluster comparative analysis. The test level α = 0.05, i.e., the difference was considered statistically significant at P < 0.05. 1)

Structural equation modeling

Structural equation modeling (SEM) is a method of statistical analysis of the relationship between potential variables and observed variables using covariance matrix. SEM is used to determine the relationship between variables through factor analysis and path analysis of relevant empirical data collected, which can reflect the role played by each indicator in the overall, and can be used to verify the validity of each indicator. The complete SEM contains two sub-models, namely: measurement model and structural model, the measurement model reflects the relationship between latent variables and the corresponding observed variables, and the structural model describes the relationship between latent variables. The formulas for the measurement model and the structural model are shown in Eqs. (8), (9) and (10).

Measurement model: 8X=Λxξ+δ$$X = {\Lambda _x}\xi + \delta $$ 9Y=Λyη+ε$$Y = {\Lambda _y}\eta + \varepsilon $$

Structural modeling: 10η=Γξ+ζ$$\eta = \Gamma \xi + \zeta $$

Where X - observed variable of ξ, ξ - exogenous latent variable, Λ_χ - matrix coefficients of link X variable to ξ variable, δ - measurement error of Measurement error of variables, Y - Observed variables of η, η - Endogenous latent variables, Λ_y - Matrix coefficients of linking Y variables to η variables, ε - Y measurement error of the variables, Γ - ξ regression coefficients of the effects of the variables on the η variables.

SPSS software was used to test the reliability and validity of the scales using reliability analysis and exploratory factor analysis. By measuring the Intercultural Factors in English and American Literary Translation scale, KMO = 0.825, Bartlett’s Test of Sphericity chi-square value = 2648.53 (p < 0.001), and Cronbach’s α = 0.861, indicating high reliability and validity of the explanatory variables measurements.

The correlation analysis was conducted after collecting the data of the relevant variables, and the results of the correlation analysis of each variable are shown in Table 2, with ** indicating that the P-value is significant at the 0.01 level and *** indicating that the P-value is significant at the 0.001 level. There is a positive and significant correlation between the variables in the cross-cultural factors of English and American literary translation (P < 0.001), and there is a negative correlation between the six cross-cultural factors and text comprehension and text consistency of English and American literary translation (P < 0.01). The hypotheses proposed in this paper were preliminarily verified.

The results of the fitness test of the model are shown in Table 3, and among the various fitness indicators, CMIN/DF, RMSEA, GFI, AGFI, NFI, IFI, and CFI all meet the fitness criteria, except for RMR which does not meet the fitness criteria. Taken together, there is a basic fit between the theoretical model and the actual data, indicating that the hypothesized model is acceptable.

Through the analysis of structural equation modeling, the standardized estimation results of path coefficients are shown in 4. The cross-cultural factors of geographic location, customs, religious beliefs, ideology, geopolitics and historical development all have a significant negative effect on text comprehension in English and American literature translation (P < 0.01), and hypotheses H1~H6 are verified. Among them, religious beliefs have the most significant effect on text comprehension in English and American literature translation, with an estimated coefficient of -0.399, followed by customs and geopolitics. The textual understanding of English and American literary translators has a significant positive effect on their textual consistency (P < 0.01) with an estimated coefficient of 0.314, and hypothesis H7 is verified. Cross-cultural factors play a role in textual coherence in translation by influencing translators’ textual understanding.