Step 1. Machine translation and Google Translate

We use Google Translate as the specific machine-translation service to evaluate the performance of machine-translated texts in bag-of-words analyses. We chose Google Translate because of its translation quality, which is top-tier when compared to other online machine translating services (Hampshire and Salvia Reference Hampshire and Salvia2010). We translated the texts using the Google Website Translator plugin which can translate web pages. To be able to use this plugin we converted the raw text data to bare html web pages. The translation process took place in August and September 2016.Footnote ⁹ We have translated the texts into English, because machine-translation algorithms are expected to perform best when translating to and from English.Footnote ¹⁰

Step 2. Preprocessing and generating TDMs

When using bag-of-words models, it is common to preprocess the data in order to remove noise. In our case we have removed punctuation, numbers and general stopwords, and all remaining words have been lowercased and stemmed. The preprocessing steps on both the gold standard and machine-translated texts are identical, and were applied to the translated texts.Footnote ¹¹ To perform these preprocessing steps, we used both Python and R libraries. For stemming, stopword removal, number removal, lowercasing, and punctuation removal, we used regular expressions in Python and the NLTK package (Bird, Klein, and Loper Reference Bird, Klein and Loper2009). To create the TDMs we switched to R and the quanteda package (Benoit and Nulty Reference Benoit and Nulty2013).Footnote ¹² We compare the TDMs of the machine-translated and gold standard documents and we also use them as input for the topics models described below. Readers primarily interested in our analysis of the TDMs may decide to skip the next section, which contains more technical details regarding the specification of our topic models.

Step 3. Fitting topic models

To assess the quality of machine-translated texts, we estimated topic models on the gold standard and machine-translated texts separately using the LDA algorithm (Blei, Ng, and Jordan Reference Blei, Ng and Jordan2003) and Gibbs sampling. For this we used the LDA function in the R topicmodels package (Hornik and Grün Reference Hornik and Grün2011). LDA is a generative model. It takes the words in each text as input and then estimates the topical prevalence and topical content in the corpus. To run the model researchers need to set a few parameters: the number of topics in the corpus, the model seed, burn-in time, the number of iterations and which and how many iterations to keep for use in the final model. To ensure that differences between a model based on the gold standard corpus and a model based on the machine-translated corpus are solely the result of language differences between these corpora, the parameters for the topic models based on gold standard translations and machine translations were kept identical. This means that the number of topics was kept constant, and a fixed seed was used—based on the sys.time variable—as suggested by Hornik and Grün (Reference Hornik and Grün2011). This seed (1473943969) has been used for all models described below. Furthermore, the burn-in (1000) and number of iterations (300) were also kept constant. The algorithm keeps every 100th model and returns the model with the highest posterior likelihood (the best-fitting model). Consequently, all variation between the models—when the model parameters are kept the same—results from differences caused by the translation process.

The most important parameter to set is the number of topics in the topic model. This is crucial because the number of topics affects the distribution of words over topics (topical content) and the distribution of topics over documents (topical prevalence). When the number of topics changes so do these distributions. It was practically infeasible to run and optimize the number of topics for each language pair. Also, all language pairs are based on roughly similar data from the same time period. Therefore the optimum number of topics for all models was determined based on the French dataset. This is the largest gold standard and machine-translated dataset. We estimated the best-fitting number of topics by evaluating the model harmonic mean of models that contain between 10 and 150 topics, in increments of 10. The model harmonic mean indicates the extent to which word counts in the documents used to construct the model match the word distributions in the model itself. Put differently, it indicates the extent to which the model accurately describes the distribution of words in the documents. In this case, a larger harmonic mean indicates that the model fits the data better. The results of the optimization runs are displayed in Figure 2. The gold standard model has an optimum of 90 topics. After 90 topics adding more topics does not improve model fit. The machine-translated model peaks at 100 topics. To isolate the effect of language differences between gold standard and machine-translated texts it is important to choose the same number of topics for both models. Therefore, we settled for 90 topics. That said, we also evaluated comparisons of models with 90 topics for the gold standard models and 100 topics for the machine-translated models. This produced results almost identical to the topic model comparisons with 90 topics. These results are available in the Supplementary Appendix.

Figure 2. Model harmonic mean.

Our next challenge is to match the topics generated by the gold standard and machine-translated models. This is because the topic order in both models may differ (i.e., topic 1 in the machine-translated model may match best with, for example, topic 2 in the gold standard model). Our matching procedure is as follows: for each stem we find the highest loading in the machine-translated topic model and the gold standard topic model. For example, take the stem “agricultur”. This stem loads highest on (is most important in) topic 12 of the machine-translated model, and topic 45 in the gold standard model. This results in a 12–45 topic pairing for that specific stem. We subsequently count the topic pairings of all shared stems. We match topics based on the highest count of topic pairings. For example, we pair topic 12 of the machine-translated model with topic 45 in the gold standard model because they have the highest number of important, shared stems like the stem “agricultur” (see the Supplementary Appendix for a numerical example of our topic matching procedure). Footnote ¹³ Using this procedure we matched 90 topics for the German corpus and 89 topics for all other languages.Footnote ¹⁴ $^{,}$ Footnote ¹⁵

Step 4. Comparing term-document matrices and topic models

We make four different comparisons, which vary on two dimensions: stems versus topics and documents versus corpora (see Table 1). The comparison of TDMs takes place at the level of stems and documents (Comparison 1 in Figure 1). Furthermore, we report three comparisons based on our topic models, all of which give us evidence on how much the matched topics in the machine-translated and the gold standard topics overlap in content and prevalence. We evaluate topical content by means of stem loadings per topic pair (Comparison 3 in Figure 1). We evaluate topical prevalence by means of topic distributions over document pairs (Comparison 2 in Figure 1), and topic distributions across the corpus at large (Comparison 4 in Figure 1).

Table 1. Comparisons between gold standard and machine-translated data.

It is important to evaluate results at both the document and the corpus level because the former only speak to how similar individual documents are being characterized by the topic model (i.e., the extent to which topical prevalence for gold standard and machine-translated documents is similar). However, such a comparison does not tell us how similar the fitted topics themselves are. For example, both the gold standard and machine-translated document might have a high topic loading on topic 1, making them highly similar on the document level, but if topic 1 is about cars in the gold standard topic model and about trees in the machine-translated model, then document-level similarity does not tell us much. While the chances of this happening are slim, structural and consistent translation errors by Google Translate might cause such differences. As a consequence, the level of topical similarity does say something about the quality of the translation. We thus need comparisons on both the document and corpus level.

Our outcome measure for the TDM comparisons is different from that of the topic model comparisons. For the TDM comparisons, we use cosine similarity because—in contrast to correlation—it takes into account the absolute differences in values. This is relevant for comparing TDMs because of our goal of knowing how similar the counts of all TDM features per document pair are to each other. Cosine similarity varies between 0 and 1, with the latter indicating a perfect match (i.e., two identical vectors). For the topic model comparisons, correlations are a more suitable similarity measure because they detect trends rather than absolute values. This is important because we make comparisons between different models.Footnote ¹⁶ Correlations vary between $-1$ and 1, with the latter indicating a perfect linear positive relationship, and the former indicating a perfect linear negative relationship.

Comparing TDMs

We first compare—at the document level—machine-translated and gold standard bags of words to each other, using the built-in similarity function in the quanteda R package (Benoit and Nulty Reference Benoit and Nulty2013). Figure 3 displays the distribution of the cosine similarity scores for each language. Most notably, the average similarity between the gold standard documents and their machine-translated counterparts is very high ( $M=0.92$ , $SD=0.07$ ). Furthermore, more than 92% of all document pairs achieve a cosine similarity score of 0.80 or higher. These results show that the TDMs of machine-translated and gold standard documents are very similar. Very often the stems in the machine-translated and gold standard documents occur with (approximately) the same frequency.

Figure 3. Distribution of cosine similarity per language pair.

Table 2 shows the means and standard deviations for document cosine similarity scores per language. The differences between languages are tiny: the lowest mean cosine similarity (Polish $=$  0.913) is only 0.016 smaller than the highest mean cosine similarity (Spanish $=$  0.929). The French and Spanish documents have significantly higher average cosine similarities than the overall mean (French: $t=7.07$ , $p<0.001$ ; Spanish: $t=5.11$ , $p<0.001$ ), but the size of these differences is, again, very small (French: 0.005 and Spanish: 0.009). The Danish, Polish and German cosine similarities between document pairs are not significantly different from the overall mean.

Table 2. Cosine similarity distribution per language.

Note: Statistically significant but substantively small difference between languages (ANOVA results: F(4, 11464) $=$  27.855, $\unicode[STIX]{x1D70C}<0.001$ , $\unicode[STIX]{x1D702}^{2}=0.010$ ).

We also consider the total number of unique stems (features), as well as the number of shared stems between the gold standard and machine-translated TDMs. The higher the number of shared stems, the more overlap there is. Figure 4 shows that the shared features of the TDMs of the gold standard and machine-translated documents overlap to a large degree (about 75% or higher). The number of shared features is also quite similar for each language (DA, 28431; DE, 27732; ES, 28578; FR, 28162; PL, 26916). The same goes for the features that are unique to either the gold standard or machine-translated TDMs.

Figure 4. Unique TDM features for gold standard and machine-translated corpora. Reading example: for the French language, the amount of overlapping features is around 28,000, while the total number of features is around 33,000 for the machine-translated documents and around 38,000 for the gold standard documents.

The exception is French, and to a lesser extent Spanish. In the Spanish case, more unique features are present in the machine-translated than in the gold standard texts, which indicates that Google Translate adds new features to the texts (by using different English translations for the same Spanish word). Similarly, French translations are simplified (different French words are translated as the same English word).Footnote ¹⁷ However, regardless of these differences, both the substantial overlap among features and the high cosine similarity scores for both Spanish and French show that their machine-translated and gold standard TDMs are highly similar.

Comparing topic models

Each document in our corpus is about one or more topics. Do the topic models with the machine-translated text as input assign the same topics to a document as the topic models with the gold standard translated texts? Figure 5 displays for each language how similar topical prevalence is for each pair of gold standard and machine-translated documents (based on an equal number of topics; for the comparison between unequal number of topics, see the Appendix). These correlations denote the extent to which topical prevalence in individual gold standard and machine-translated documents overlaps. The higher the correlation the more the overlap.Footnote ¹⁸ It shows that document-level topical prevalence is similar for gold standard and machine-translated corpora, with on average—across all languages—65% of document pairs having a topic distribution correlation of 0.8 or higher. Put differently, a particular document is likely to be assigned to identical topics regardless of whether it was machine-translated or gold standard translated.

Figure 5. Similarity of document-level topical prevalence with equal number of topics.

That said, there are statistically significant differences between languages (see Table 3).Footnote ¹⁹ Table 3 breaks down mean topical prevalence for each language, as well as their standard deviations. The highest mean topic distribution per document pair is obtained for Spanish (0.83), and the lowest for French (0.75). Again, the absolute differences are small, and across languages it appears that topical prevalence at the level of individual documents is similar.

Table 3. Similarity of document-level topical prevalence with equal number of topics.

Note: ANOVA results: F(4, 11464) $=$  56.414, $\unicode[STIX]{x1D70C}<0.001$ , $\unicode[STIX]{x1D702}^{2}=0.019$ .

Each topic in our data is discussed in several documents. Are these the same documents in the topic models of the machine-translated text and the gold standard translations? To evaluate this we calculate the correlations between the topical prevalence of each topic in the gold standard and the machine-translated documents (Figure 6 show the results of 446 topic distribution comparisons).Footnote ²⁰ As in the case of document-level topic distributions, these corpus-level correlations are generally quite similar, having a mean of 0.69. This indicates that on average topics are similarly distributed across all documents in the corpus. This indicates that a topic is likely to be distributed similarly across documents, regardless of whether these documents where machine translations or gold standard translations of the same source.

Figure 6. Similarity of corpus-level topical prevalence with equal number of topics. Overall descriptives: $N=446$ , $M=0.699$ , $SD=0.321$ .

Finally, we also compare the similarity in the content of paired topics. To do so, we analyze for each topic pair the stem loadings of all shared features in the gold standard and machine-translated TDMs. The results are presented in Figure 7. Again, the average correlation is about 0.70 across languages indicating that topical content, as measured by the distribution of stem loadings, is similar for both the machine-translated and the gold standard corpora.Footnote ²¹ That implies that topics are discussed using the same terms in both the machine-translation and gold standard translation documents.

Figure 7. Similarity of topical content with equal number of topics. Overall descriptives: $N=446$ , $M=0.708$ , $SD=0.345$ .