Using Spelling Error Analyses to Examine Individual Differences in German Students From Diverse Linguistic Backgrounds: A Latent Class Approach

Abstract

The current study examined German spelling errors among students with German as their first language (L1) and those with German as their second language (L2) in Grades 3–4 (elementary school students; n = 127) and Grades 5–7 (secondary school students; n = 379). Five hundred and six students participated in the study. We performed two separate latent class analyses on elementary and secondary school students. Results indicate that elementary school students can be categorized as good (Class 1), consonant error dominant (Class 2), or poor (Class 3) spellers. However, secondary students can be categorized as addition and sequence error dominant (Class 1), substitution and omission error dominant (Class 2), or poor (Class 3) spellers. The three-step multinomial logistic regression analyses suggested that decoding was associated with the highest chances of being poor spellers in both elementary and secondary schools. Speaking German as L1 or L2 was a significant predictor of heterogeneities in secondary, but not elementary, school students. Polish L1 secondary students had the highest possibility of being poor spellers. The results suggest heterogeneities of student profiles. In addition, special attention should be given to secondary school students with the Polish L1 background in their spelling struggles associated with German orthography.

Keywords

German spelling latent classification orthography second language

Spelling is closely related to concurrent and longitudinal reading development and is a fundamental skill for written composition because inaccurate and effortful spelling drains attention needed for planning, generating ideas, formulating sentences, and self-regulating during the writing process (Berninger et al., 1992). Therefore, spelling proficiency has been acknowledged as an indicator of literacy development and has been used as one of the most important screening criteria for learning disabilities (Berninger et al., 1992). Spelling research studies have primarily focused on English orthography. However, German spelling research has been given less attention, which may be problematic because different orthographies may have different features that influence spelling proficiencies (Goswami et al., 2005). In English, the grapheme-to-phoneme correspondence (GPC) and phoneme-to-grapheme correspondence (PGC) are opaque, which may cause challenges to both reading and spelling. In German, the PGC patterns are much less transparent than the GPC rules are, suggesting that German spelling may be more challenging to acquire than reading is (Goswami et al., 2005).

Based on the original spelling stage theory (Ehri, 1997), Valtin (1997) categorized spellers based on primary strategies used in different stages and identified six developmental phases: (1) the figurative strategy stage, (2) logographic strategy stage, (3) beginning phonetic strategy stage, (4) phonetic-articulatory strategy stage, (5) phonemic strategy with orthographic awareness, and (6) complete phonemic strategy with orthographic and morphological awareness. Students in the beginning phonetic strategy stage start to use letter names as cues to represent sounds (e.g., ehs for ich [I]). Individuals in the phonemic-articulatory stage understand the GPC principle but often commit substitution, omission, and addition errors, especially in words with digraphs and nasalized vowels (e.g., aien for ein [one/a]; ben for bin [am]; lesn for lesen [read]). Students in the phonemic strategy with orthographic awareness have fewer omission and substitution errors but tend to overgeneralize syllable patterns, thus making orthographic errors (oper for opa [grandpa]). Students in the final spelling stage have mastered orthographic rules and can adjust spelling based on morpheme-syntactical context (e.g., Hand—Hände [hands]; Valtin, 1997).

Spelling Error Analysis

The stage theories have provided important information on how students develop from prephonemic to proficient spellers from a general perspective. However, critics have suggested that the stage theories oversimplify the developmental spelling patterns and do not consider orthographic features and individual differences (Treiman & Kessler, 2014). Recent researchers have used spelling error analysis to provide richer information on individualized weaknesses and thus inform instructional foci for different students. Some of them have classified spellings into phonological, orthographical, etymological, and morphological categories to examine the role of meta-linguistic processing (e.g., Bahr et al., 2020). Other researchers have focused on the number of phonemes correctly represented in spelling (e.g., Lee & Al Otaiba, 2017). On the other hand, Treiman’s (1993) method concentrated on the interaction between linguistic properties and spelling proficiency. Treiman categorized vowel and consonant errors into substitution, omission, and (adjacent) letter sequence errors, and Zhang et al. (2021) further included vowel and consonant addition errors. In fact, vowels and consonants have various acoustic properties that may influence spelling differently and cause different types of spelling errors (Moats, 2010). This method was later adapted for spelling error analysis in different orthographies (e.g., Stage & Wager, 1992; Wimmer & Landerl, 1997). In addition, individual developmental differences that are independent of the spelling stage theory have been observed. For example, Zhang et al. (2021) conducted latent classification analysis (LCA) on Spanish spelling errors and found vowel and consonant spelling did not develop in tandem because the former was easier to acquire; however, individual differences were observed in each grade level because some students performed well below their grade-equivalent counterparts in spelling. Therefore, investigation of spelling development needs to consider orthographic features (e.g., vowel vs. consonant) and individual developmental differences rather than just the features of each stage.

Vowel Spelling Errors

In English and German, each vowel letter has a short and long sound, and some vowel sounds are similar in tongue positions (front, central, and back) and mouth shapes (close, mid-close, mid-open, and open; Moats, 2010). English phonology contains around 15 vowel phonemes (Moats, 2010). Treiman (1993) found that vowel phonemes /ɛ/ (pet) and /I/ (pit) elicit many English vowel substitution spelling errors among first graders (e.g., lit for let), because both are mid-close, front vowels. German has around seven short vowel phonemes and eight long vowel phonemes, and some diphthongs, r-controlled phonemes, and unstressed vowels (Landerl, 2003). Like English, German vowel sounds can share similar tongue positions and mouth shapes (e.g., front vowels /ɛ/ vs. /I/). The /ɛ/ sound can also correspond to ä as in Bälle (balls) and e as in Welle (wave; Wimmer & Landerl, 1997). Interestingly, previous studies have suggested that German first-grade students, including students with dyslexia, did not show substantial vowel substitution errors (Wimmer, 1993; Wimmer & Landerl, 1997).

In English, vowel omission errors tend to occur on long vowels (Treiman, 1993). Early grade students tend to use vowel letter names to spell long vowels but omit vowel markers such as vowel digraphs and the silent e (Bear et al., 2015; Lee & Al Otaiba, 2017; Treiman, 1993). As a result, vowel omission errors frequently occur on vowel digraphs (e.g., bal for bail) and silent e syllables in English (e.g., cak for cake; Bear et al., 2015; Treiman, 1993). In German, silent vowel cases are rare, and the ending letter e is usually pronounced (e.g., Nase [nose]: /nɑzə/; Wimmer & Landerl, 1997). In addition, word context gives clues to whether a vowel should be marked as long. For example, long vowels are usually marked by vowel digraphs or vowel-h (e.g., Meer [sea]; Stuhl [chair]), whereas consonant blends and doublets follow short vowels (e.g., Pfund [pound] Wunsch [wish]; Ritter [knight]). Landerl (2003) found that German 10-year-olds with dyslexia committed substantial long vowel errors, such as marking a long vowel with a single vowel letter, suggesting deficiencies in applying orthographic knowledge in vowel spelling. Vowel-marking errors thus may be an essential risk factor for dyslexia.

Vowel addition errors are often related to the overgeneralization of complex vowel patterns. Bernstein (2009) suggested that students with sufficient phonemic awareness but difficulties in differentiating syllables in spelling may use vowel digraphs or the silent e to represent single-vowel graphemes and thus commit vowel addition errors (e.g., plane/plain for plan). Because many German long vowel sounds are marked by vowel digraphs (e.g., Meer [sea]), such addition errors may also occur in German spelling. However, the prevalence of vowel addition errors in German spellers has never been examined.

Consonant Spelling Errors

Per linguistic studies, consonant sounds differ on place (e.g., bilabial, palatal, and velar) and manner of articulation (e.g., voiced vs. voiceless; stops vs. fricative sounds; Moats, 2010; Treiman, 1993). Across orthographies, consonant substitution errors tend to occur between sounds that share similar acoustic and visual features. For example, b and d are stop sounds and have similar letter shapes, thus leading to substantial b/d substitution errors across alphabetic orthographies (Treiman, 1993; Zhang et al., 2021). Therefore, differentiating similar consonant sounds is important to overcome consonant substitution errors. In addition, terminal devoicing is a unique orthographic feature in German, which means a voiced consonant at the end of a word can be voiceless. For example, letter d may produce a /t/ sound at the end of a syllable, and students can make /t/ and /d/ substitution errors due to this orthographic feature (Berkling & Lavalley, 2018).

In English, consonant omission errors tend to occur on consonant blends from unstressed syllables (e.g., playgound for playground; Treiman, 1993). In German, however, Wimmer and Landerl (1997) found that typical and poor spellers in first grade did not commit many errors on consonant blends. Such analysis needs to be reexamined in older students who face spelling tasks that are more challenging. Consonant doubling is another potential factor that may elicit consonant omission errors. In English and German, a middle consonant is doubled in a two-syllable word when it has a preceding short vowel and has only one consonant sound between the two vowels (i.e., the “rabbit rule”); an f, s, or l letter is also doubled when it appears at the end of a monosyllable word after a short vowel (i.e., the “floss rule”; Bitte [please]; Ball [ball]; Landerl & Reitsma, 2005). However, some exceptions also apply. For example, when a medial z has a /ts/ or /k/ sound, it is not doubled but corresponds to a tz (Katze [cat]) or ck (Backe [cheek]) grapheme (Landerl & Reitsma, 2005). In addition, consonant trigraphs in high-frequency German words, such as Schritt (step) or Schriftsteller (writer), may also elicit chances of consonant omission errors. Therefore, consonant errors may still be prevalent in upper grades.

Similar to vowels addition, consonant addition errors may occur due to the overgeneralization of spelling patterns (Valtin, 1997). For example, Valtin (1997) found that some students tend to write opa (grandpa) as opar. Students may also erroneously add a silent h after a short vowel, reflecting a confusion of vowel markers for different vowel durations (Klicpera & Schabmann, 2013).

Sequence Errors

Treiman (1993) noted that adjacent letter sequence errors could appear in vowel-liquid and vowel-nasal letter combinations (e.g., hre for her; mlik for milk) due to the difficulties in segmenting and sequencing vowel-liquid and vowel-nasal phoneme combinations. Graphotactic factors may also be associated with sequence errors (Treiman & Kessler, 2014). In the “hre for here” case, Treiman (1993) suggested that students might be influenced by the frequency of other words with a re ending such as here, are, sure, care, and were. Treiman (1993) also found some students wrote vowel digraphs and consonant digraphs in an erroneous sequence (e.g., lest for lets; jeoy for joey).

Individual Differences in Vowel and Consonant Acquisition

In summary, vowel and consonant errors are closely related to orthographic features. These features may lead to different error frequencies in vowel and consonant categories in different orthographies. In English, Stage and Wagner (1992) administered 22 phonetically regular pseudowords to students in kindergarten to Grade 3 and found that mid-to-low vowels such as /ʌ/ and /ɜ/ had the most errors, whereas the performance on consonants was consistently better. In German, despite the difficulties in differentiating vowel markers in spelling for some students, it is believed that vowels are still easier to spell than English vowels are. On the other hand, given the prevalence of consonant digraphs, trigraphs, and terminal devoicing in higher grades, consonant spelling may lead to substantial errors even in older, more proficient students.

However, less is known about the heterogeneity of spelling profiles. Because long vowels were found difficult for students with risks of dyslexia (Landerl, 2003), using person-centered, heterogeneity-probing analysis, we may find individual differences in spelling development and identify students with risks of dyslexia. Students who find long vowel markers difficult may need more targeted intervention on early literacy skills.

Role of Decoding and Home Language in Individual Spelling Profile Differences

According to Bear et al. (2015) and Ehri (1997), spelling and decoding grow in tandem because they come from shared knowledge, including alphabetic and phonic skills. However, because German has a less transparent PGC than GPC, German students may develop spelling accuracy slower than they develop decoding accuracy. For example, Landerl and Wimmer (2008) found that German students had a high decoding accuracy in Grade 1 but much lower spelling proficiency. Currently, few studies have examined whether decoding could be a significant factor in differentiating proficient and striving spellers. It is understood that students in Grade 3 and higher have generally mastered the phonetic structure and are transitioning to conventional spelling (Bear et al., 2015; Valtin, 1997). However, if we found a possibility of heterogeneity in spelling profiles and poor spellers were making substantial omission and substitution errors, then decoding might be a significant factor explaining this poor performance.

Earlier studies have suggested that German L2 learners had lower spelling proficiency than their L1 counterparts had (Festman & Schwieter, 2019). In addition, Breuer (2017) found that adult German L2 students performed significantly poorer than L1 students did in spelling and writing tasks. Bassetti (2017) suggested that the orthographic similarity between L1 and L2 might influence L2 spelling proficiency. For example, L1 Arabic German learners may be influenced by reading from right to left, thus making more sequence errors than students reading from left to right in both L1 and German do. In addition, L1 phonology can have an influence on L2 German spelling. For example, Polish, Russian, and Turkish do not have long and short vowel differentiation (Darcy & Krüger, 2012; Nimz & Khattab, 2019). Hence, Polish, Russian, and Turkish German learners may be less sensitive to spelling patterns that are cued by vowel durations.

The Current Study

Per Treiman (1993) and later development of the error classification method (e.g., Zhang et al., 2021), this study adopted vowel-based and consonant-based spelling errors as two umbrella categories and further categorized each error into substitution, omission, addition, and sequence error categories. We proposed four research questions (RQ); each was followed by a hypothesis:

Research Question 1 (RQ1): Are consonant errors more prevalent than vowel errors are in German Grades 3 through 7? We hypothesized that consonant errors would be more prevalent than vowel errors would.

Research Question 2 (RQ2): What are the latent classifications and characteristics of German spellers? We hypothesized that heterogeneities of spelling performance would occur in both elementary and secondary students.

Research Question 3 (RQ3): Are decoding and home language status (German L2 vs. L1) associated with the heterogeneous profiles? We hypothesized that both would be predictive of spelling heterogeneities.

Finally, we also scrutinized the specific L1s that have higher error possibilities, leading to

Research Question 4 (RQ4): Which L1 was associated with specific error patterns as operationalized by different latent classes? We hypothesized that L1-Turkish, L1-Polish, and L1-Arabic students would have higher chances of German spelling difficulties than other L1s.

Method

Participants

A total of 506 students (originally 507, one dropped out during the study) from Grades 3 through 7 across seven schools in the state of North Rhine-Westphalia participated in the study. This project was derived from the third author’s service work provided to the state of North Rhine-Westphalia. The participants attended either an elementary school (Grades 3–4; Grundschule, preparing students for different types of secondary schools) or a secondary school (Grades 5–7; Gesamtschule, preparing secondary school students for colleges or vocational schools). All students from Grades 3 through 7 in these seven schools were invited, but different numbers of teachers and students in each grade agreed to participate in the study. The second and third authors led the data collection, and 12 graduate students were trained to collect the assessment data.

None of the schools offered bilingual classes, and school instruction was in German only. We first surveyed the participants and their parents about their birthplace. Parents who reported being born outside Germany were additionally asked to specify their preferred home language. For the parents who reported speaking a language other than German at home, we asked about their children’s reading and writing proficiency. Based on the survey item results, we defined German L1 speakers by the following criteria: (a) having both parents born in Germany and (b) having parents who speak German at home. We defined German L2 speakers as follows: (a) the student or at least one parent was born outside Germany, (b) parents speak a language other than German at home, and (c) students have at least a beginning-level literacy skill in their L1. Participants who did not fit into any of the categories or who gave contradictory answers would be dropped from the analysis, which did not occur in the current research.

We identified 290 (57.31%) German L1 students and 206 German L2 students based on the survey. The most common L1s other than German were Turkish (n = 61), Arabic (n = 43), Polish (n = 27), and Russian (n = 20). Table 1 includes the common L1s in each grade level. Other L1s included Serbian (n = 11), Persian (n = 7), Kurdish (n = 7), Spanish (n = 7), Romanian (n = 5), Italian (n = 4), Bosnian (n = 3), Congolese (n = 3), Portuguese (n = 3), French (n = 2), Romani (n = 2), Albanian (n = 1), Armenian (n = 1), Chinese (n = 1), Croatian (n = 1), Greek (n = 1), Hungarian (n = 1), Kazakh (n = 1), Lebanese (n = 1), Pakistani (n = 1), Sinti (n = 1), and Togolese (n = 1). The percentage of German L2 students at each grade (3–7) was 69%, 53%, 26%, 44%, and 8%, respectively. The percentages of females across the five grade levels were 43.30% (Grade 4) to 62.50% (Grade 7). Table 2 shows detailed demographic data.

Table 1.

Distribution of Major L1s (Proxied by Home Language Preference).

Grade level	Home language
Grade level	German	Turkish	Arabic	Polish	Russian	Other L1
3 (n = 67)	21	5	12	3	9	17
4 (n = 60)	28	6	5	3	1	17
5 (n = 133)	99	8	4	7	6	9
6 (n = 233)	130	41	22	14	4	22
7 (n = 13)	12	1	0	0	0	0
Total (N = 506)	291	61	43	27	20	65

Table 2.

Demographic Information and Descriptive Statistics of Errors (Mean and Variance).

Grade	Age (Variance)	Females (%)	German L2 (%)	CS (Variance)	CO (Variance)	CA (Variance)	CSEQ (Variance)	VS (Variance)	VO (Variance)	VA (Variance)	VSEQ (Variance)
Grades 3–4
3 (n = 67)	9.07 (0.53)	33 (49.30)	46 (68.66)	10.94 (49.30)	7.70 (24.91)	3.82 (9.39)	0.42 (0.49)	2.78 (8.90)	1.51 (3.92)	0.87 (11.06)	0.07 (0.10)
4 (n = 60)	9.88 (0.44)	26 (43.30)	32 (53.33)	8.95 (51.30)	7.20 (42.81)	3.43 (7.61)	0.25 (0.23)	2.25 (6.46)	1.63 (4.00)	0.52 (0.59)	0.07 (0.10)
Total (n = 127)	9.46 (0.80)	59 (46.5)	78 (61.42)	10.00 (50.84)	7.46 (33.16)	3.64 (8.51)	0.34 (0.37)	2.53 (7.76)	1.57 (3.93)	0.70 (6.10)	0.07 (0.10)
Grades 5–7
5 (n = 133)	10.92 (0.49)	62 (46.60)	34 (25.56)	21.05 (178.16)	18.39 (190.10)	9.33 (58.73)	0.56 (5.82)	9.78 (50.45)	6.16 (31.65)	2.83 (7.17)	0.20 (1.19)
6 (n = 233)	11.68 (0.61)	103 (44.21)	103 (57.08)	14.38 (176.20)	13.88 (212.50)	8.67 (61.91)	2.63 (41.12)	6.96 (57.21)	4.48 (28.91)	2.82 (8.94)	0.45 (3.53)
7 (n = 13)	12.69 (0.40)	8 (6.50)	1 (7.69)	6.46 (31.27)	5.85 (31.97)	2.85 (4.97)	0.23 (0.19)	4.15 (10.97)	2.31 (7.23)	1.69 (1.23)	0.00 (0.00)
Total (n = 379)	11.45 (0.74)	173 (45.50)	138 (36.41)	16.44 (185.33)	15.18 (205.84)	8.70 (60.02)	1.82 (28.37)	7.85 (55.36)	4.99 (29.91)	2.78 (8.08)	0.35 (2.60)

Note. Grades 3–4 and 5–7 separated due to receiving different tests. CS = Consonant Substitution; CO = Consonant Omission; CA = Consonant Addition; CSEQ = Consonant Sequence Errors; VS = Vowel Substitution; VO = Vowel Omission; VA = Vowel Addition; VSEQ = Vowel Sequential Errors.

Procedure

Screening and nonword decoding

The second and third authors and 12 graduate students administered two reading tests to screen for literacy disabilities for a larger project, which were the Pseudoword (Nonword) and Word Reading subtests from the Salzburg Reading and Orthography Test II (Moll & Landerl, 2010). Both tests have high test–retest reliability coefficients across grades (.80 and .97) and correlate highly (r ≥ .75) with the Salzburg Reading Screening Instrument (Breuer, 2017). Based on the two tests, the current sample had a number of students at risk for reading disabilities. Of the 506 participants, 110 (21.70%) fell below the 15th percentile in the Pseudoword Reading Subtest, and 141 (27.81%) fell below the 15th percentile in the Word Reading Test. The correlations between nonword and word reading tests were high (r = .81 for elementary grades and r = .84 for secondary grades), suggesting they reflected similar abilities. Due to the high correlation, we chose to use the nonword decoding scores from the Salzburg Reading and Orthography Test II to proxy decoding. This decision was made to reflect the role of German GPC skills in spelling more precisely, because real-word decoding skills might also be influenced by sight word knowledge (Ehri, 1997).

The nonword-decoding test from SLRL II consisted of 156 two-syllable and three-syllable phonetically regular nonwords. The first 20 nonwords had four letters with two consonants, and two were vowels. Starting from the 21st word, vowel and consonant digraphs and trigraphs begin to emerge to form nonwords, but these graphemes are all highly frequent in the German lexicon. For example, the nonword schmane in this test contained a frequent consonant trigraph sch as found in schmecken (taste) and schmuck (jewelry).

Spelling tasks and error classifications

For the elementary school students (Grades 3–4), we administered the German Orthography Test for Third and Fourth Graders (DERET 3–4; Stock & Schneider, 2008; parallel-form reliability = .95); for the secondary school students (Grades 5–7), we administered the German Orthography Test for Fifth and Sixth+ Graders (DERET 5–6+; Martinez Méndez et al., 2015; test–retest reliability = .95). The different versions of the DERET are quite widely used in German school psychology and related fields to measure students’ orthographic skills. They are each based on the curriculum benchmarks of the 16 German states. Both tests require participants to write sentences that are dictated to them, consisting of words taken from a pool of the most common words used in the German language. The syntactical complexity of the dictated sentences is simpler in DERET 3–4 than it is in DERET 5–6+.

After the complete tests were administered, we classified the spelling errors from DERET 3–4 and DERET 5–6+ into the earlier specified clusters that have often been used successfully in previous studies to categorize orthographic errors (Zhang et al., 2021): (a) consonant substitution (e.g., Fergessen for Vergessen [forget]), (b) consonant addition (e.g., Krieschen for Kriechen [crawl]), (c) consonant omission (e.g., Je_zt for Jetzt [now]), (d) consonant sequence (e.g., Troztdem for Trotzdem [regardless]), (e) vowel substitution (e.g., Sterke for Stärke [strength]), (f) vowel addition (e.g., Wiederlich for Widerlich [obnoxious]), (g) vowel omission (e.g., Spilen for Spielen [play]), and (h) vowel sequence errors (e.g., Phenomän for Phänomen [phenomenon]). The standard analysis of the two DERET versions grouped spelling mistakes into 12 categories. However, unlike our chosen strategy, this way of grouping errors has not been used in previous research to compare the orthographic skill levels of L1 and L2 learners.

Analytic method

We conducted LCA to examine the classification of spellers based on the eight spelling error categories. We first examined each error variable’s mean and variance to determine the distribution type of spelling errors. Spelling-error count data are discrete, non-negative, and often positively skewed. Thus, we initially planned to model LCAs on Poisson distribution rather than a normal distribution (Agresti, 2007). However, the mean and variance should be roughly the same in Poisson distributions (i.e., mean and variance share one parameter; Agresti, 2007). Across the eight spelling error categories, the variance of each error was much higher than its mean was (see Table 2). The overdispersion of data allowed us to apply a negative binomial distribution, an extension of Poisson distribution, on these eight count variables. In analysis with a negative binomial distribution, mean and variance are separate parameters and thus allow these two parameters to differ. In addition, a dispersion parameter is added to the mean to reduce overdispersion’s influence on estimations (Hilbe, 2012).

To address RQ 1, we used descriptive statistics from Table 2 to compare consonant and vowel error amounts and distributions. To address RQ 2, we first modeled the eight spelling-error count variables for LCA estimation and sought to determine the number of distinct types of spellers using negative-binomial-distribution-based LCA. To determine the number of latent classes among the students, we examined Akaike information criterion, Bayesian information criterion (BIC), and sample-size-adjusted BIC (SBIC) values. Lower criteria values would indicate a better model fit. We also applied the Lo–Mendell–Rubin test and the bootstrap likelihood ratio test to compare the fit of the current number of classes (K) with the K−1 number of classes. Significant Lo–Mendell–Rubin or bootstrap-likelihood ratio results would indicate a model fit improvement after adding classification. If these statistics were unable to provide a clear latent class solution, then we would compare practical meaningfulness of the solutions to make a decision.

To address RQ 3, we regressed the latent spelling proficiency classifications on nonword decoding (continuous variable) and home language status (L2 vs. L1), after controlling for grade level (ordinal) and gender (female vs. male). Similar to above, elementary and secondary students were fitted in different models. A regression coefficient would be interpreted as the predictive power of a variable in explaining the chance for students to be classified into one classification versus another. Our goal in this step was to understand potential student factors associated with latent classifications; thus, we kept the latent classifications constant when examining the predictive powers of student factors. Therefore, we adopted a three-step regression approach (Bolck et al., 2004), which includes determining the latent class membership (Step 1), estimating the uncertainty of classification through calculating standard errors of the solution (Step 2), and holding the estimated classification and standard errors constant when fitting the regression model (Step 3). If the LCA solutions suggested more than three latent groups, then the regression model would become a three-step multinomial logistic regression with one class being a reference group. We would choose the lowest-performing group as the reference group. Odds ratios (OR) would be used to interpret the predictive powers of nonword decoding, language status, grade level, and gender in explaining the chances of being poor spellers versus other spellers (“better spellers”). An odds ratio greater than 1 would indicate a greater chance of being in the better group, and smaller than 1 would indicate a greater chance of being in the poor speller group. We applied maximum likelihood with robust standard error to LCA to address missing data. Because one class was compared at least twice (e.g., poor vs. Class 1; poor vs. Class 2), we chose the Benjamini–Hochberg adjustment (Benjamini & Hochberg, 1995) method to control the false discovery rate in testing multiple comparisons.

To answer RQ 4, the posterior classifications from the above LCA analyses were scrutinized. We calculated the proportion of each L1 in each latent group against the total number of students in that L1 and compared the proportions across different L1s using chi-square tests within each latent classification. Because the participants had many different L1 backgrounds, we focused on L1s with larger sample sizes, including German, Turkish, Arabic, Polish, and Russian. The rest were grouped as “other L1s.” In addition, as these chi square tests involved many paired comparisons, we again applied Benjamini–Hochberg corrections to improve the accuracy of probability values. We performed all analyses with Mplus version 8.3 (Muthén & Muthén, 2019).

Results

Consonant and Vowel Errors

In the elementary school sample (Grades 3–4), the 127 students committed 3,341 errors: 2,723 consonant errors and 618 vowel errors. Each student on average made 26.31 errors: 21.44 consonant errors and 4.87 vowel errors. As shown in Table 2, consonant substitution was the most frequent error because each student on average committed 10 errors (total errors = 1,270). Vowel sequence was the least frequent error, with an average of 0.07 per student (total errors = 9). In the secondary school sample (Grades 5–7), the 379 students committed 22,086 errors: 16,017 consonant errors and 6,069 vowel errors. Each student on average made 58.12 errors: 42.15 consonant errors and 15.97 vowel errors. Consonant substitution was the most frequent error because each student on average committed 16.43 errors (total consonant substitution errors = 6,248). Vowel sequence was the least frequent error with an average of 0.35 per student (total vowel sequence errors = 132; see Table 2).

Latent Classifications of Spellers in Elementary and Secondary Schools

A series of Lo–Mendell–Rubin tests showed that for both elementary and secondary school students the three-class solutions were significantly better than were the two-class solutions, but the four-class solutions did not show an improvement over the three-class solutions (see Table 3). However, the bootstrap-likelihood ratio test showed that the four-class solutions were better than the three-class solutions. Due to the conflicting results, we further examined the three-class and four-class posterior solutions to compare the practical meaningfulness to make a final decision on the solution.

Table 3.

Comparing Latent Class Solutions for Grades 3–4 and Grades 5–7 Students.

Measure	Grades 3 & 4						Grades 5–7
Measure	1-Class	2-Class	3-Class	4-Class	5-Class	6-Class	1-Class	2-Class	3-Class	4-Class	5-Class	6-Class
AIC	3,711.20	3,549.43	3,501.59	3,463.67	3,443.93	3,459.70	15,708.17	15,013.73	14,663.59	14,322.14	14,076.94	13,956.58
BIC	3,756.71	3,620.54	3,598.29	3,585.97	3,591.83	3,633.19	15,771.21	15,112.23	14,797.55	14,491.57	14,281.83	14,196.93
SABIC	3,706.11	3,541.48	3,490.77	3,449.99	3,427.38	3,440.28	15,720.45	15,032.91	14,689.68	14,355.14	14,116.84	14,003.39
Entropy	NA	0.83	0.86	0.90	0.90	0.91	NA	0.89	0.87	0.92	0.91	0.91
Loglikelihood value	–1,839.60	–1,749.72	–1,716.79	–1,688.84	–1,669.97	–1,668.85	–7,838.09	–7,481.86	–7,297.79	–7,118.07	–6,986.47	–6,917.29
Scaling correction factor for MLR	1.32	1.25	1.14	1.00	0.99	0.82	1.07	1.25	1.43	1.57	1.51	1.66
2 times loglikelihood value difference^a	NA	180.16	94.68	56.22	59.79	30.29	NA	712.44	368.14	359.45	263.20	138.36
Number of parameter difference^a	NA	10	11	14	23	23	NA	9	9	9	9	10
LMR p-value of difference^a	NA	**	*				NA	***	*
BLRT p-value of difference^a	NA	***	***	***	***	***	NA	***	***	***	***	***

Note. Bolded columns indicate final selected model. AIC = Akaike’s Information Criteria; BIC = Bayesian Information Criteria; BLRT = Bootstrap likelihood ratio test; LMR = Lo-Mendell-Rubin likelihood ratio test; MLR = Maximum likelihood with robust standard error; K = Number of classes; SABIC=Sample-size-adjusted Bayesian Information Criteria.

K vs. K-1 class.

p < .05. **p < .01. ***p < .001.

For both the four-class solutions for the elementary and secondary students (see Figure 1), profiles overlapped in every error category. For elementary school students, Classes 1 and 4 showed similar estimated error counts on consonant and vowel sequence and addition errors, and Classes 2 and 3 had similar performances on vowel categories. For secondary school students, Classes 1 and 2 as well as Classes 2 and 4 had a similar estimated number of vowel addition and sequence errors. Classes 2 and 3 had a similar estimated number of omission errors. On the other hand, despite a few overlaps on vowel addition and sequence categories, the classifications of each category were more evident using the three-class solutions (see Figure 1). Therefore, we chose the three-class solutions as the final models for the elementary and secondary school students. The complete estimations from three-class solutions, including sample sizes of latent classes (n), the original logits and transformed error counts (n_e), and standard errors of estimations (SE), are reflected in Table 4.

Table 4.

Results of the Three-Class Solution.

Error type	Grades 3 & 4									Grades 5–7
	Good^a			Consonant ED^b			Poor^c			Addition & sequence ED^d			Substitution & omission ED^e			Poor^f
	Logit	n _e	SE	Logit	n _e	SE	Logit	n _e	SE	Logit	n _e	SE	Logit	n _e	SE	Logit	n _e	SE
CS	1.89	1.40	0.33	1.06	6.63	0.20	2.80	16.48	0.08	0.34	2.90	0.13	2.54	12.64	0.10	3.43	30.75	0.08
CO	1.58	1.54	0.25	1.06	4.87	0.13	2.50	12.23	0.12	0.43	2.90	0.18	2.36	10.62	0.10	3.39	29.76	0.10
CA	1.11	0.81	0.47	2.34	3.02	0.18	1.65	5.20	0.09	–0.21	10.33	0.14	1.72	5.61	0.12	2.49	12.01	0.08
CSEQ	–1.57	0.00	<0.01	1.99	0.21	0.39	–0.53	0.59	0.20	–26.37	7.30	0.18	–1.54	0.21	0.21	–0.69	0.50	0.20
VS	0.47	0.47	0.39	0.28	1.61	0.14	1.44	4.21	0.17	–0.76	1.32	0.14	1.71	5.55	0.11	2.74	15.43	0.09
VO	0.08	0.27	0.89	–0.09	1.08	0.20	0.93	2.52	0.19	–1.32	0.91	0.25	1.16	3.18	0.13	2.33	10.25	0.11
VA	–0.95	0.00	0.00	1.34	0.39	0.23	0.24	1.27	0.43	–26.05	3.82	0.14	0.73	2.08	0.07	1.13	3.10	0.10
VSEQ	–3.47	0.12	1.01	0.26	0.03	0.89	–2.30	0.10	0.52	–2.09	1.29	0.30	–3.01	0.05	0.40	–1.90	0.15	0.46

Note. ED = Error Dominant; SE = Standard Errors of Estimations; CS = Consonant Substitution; CO = Consonant Omission; CA = Consonant Addition; CSEQ = Consonant Sequence Errors; VS = Vowel Substitution; VO = Vowel Omission; VA = Vowel Addition, VSEQ = Vowel Sequence Errors; n_e = Number of estimated errors.

n = 15. ^bn = 59. ^cn = 53. ^dn = 80. ^en = 183. ^fn = 116.

As shown in Table 4, for elementary school students, the three-class solutions reflected more ability-level differences. Class 1 (12%; n = 15; total n_e = 4.61; n_e < 1 across categories) made the least number of estimated errors across categories, and Class 3 (42%; n = 53; total n_e = 34.95) made the highest number of estimated errors overall, especially on consonant substitutions (n_e = 16.48) and consonant omissions (n_e = 12.23). We therefore labeled Class 1 as good spellers and Class 3 as poor spellers. Class 2 (46%; n = 59; total n_e = 34.95) had comparable performances with good spellers on vowel categories (n_e < 2) but more errors than good spellers on consonant substitution, omission, and addition (n_e = 3.02–6.63). Therefore, we labeled Class 2 as consonant error dominant spellers.

Among secondary school students, Class 3 (31%; n = 116) struggled the most as indicated by the fact that they had the largest number of errors (total n_e = 101.95); thus, we labeled them as poor spellers. Classes 1 and 2 had much fewer errors than poor spellers had (Class 1 total n_e = 30.37; Class 2 total n_e = 39.94). However, Classes 1 and 2 had different performances in different categories: Class 1 made a larger amount of consonant and vowel additions (consonant addition: n_e = 10.33; vowel addition: n_e = 3.82) and sequence errors (consonant sequence: n_e = 7.30; vowel sequence: n_e = 1.29) than did Class 2. These students were labeled addition and sequence error dominant spellers. Class 2 had larger number of substitution (consonant substitution n_e = 12.24; vowel substitution n_e = 5.55) and omission errors (consonant omission: n_e = 10.62; vowel omission: n_e = 3.18) than Class 1 did. Therefore, these students were labeled substitution and omission error dominant spellers.

Predictors of the Heterogeneity

The three-step logistic regression analysis suggested that for elementary school students, decoding was a significant predictor in explaining the differences between consonant error dominant spellers versus poor spellers (OR = 1.07; 95% CI = [1.01, 1.12]) and good versus poor spellers (OR = 1.15; 95% CI = [1.09, 1.25]). The odds ratios suggested that students who scored 1 point higher in nonword decoding had a 7% greater chance of being consonant error dominant spellers as opposed to poor spellers and a 15% greater chance of being good spellers rather than poor spellers. In the elementary school sample, grade level, home language, and gender did not have significant predictive powers of the latent spelling classifications (see Table 5).

Table 5.

Predictive Power of Nonword Decoding, Language Status and Grade Level on the Classification.

Grades 3–4	OR	SE	Sig.	Grades 5–7	OR	SE	Sig.
Consonant error dominant vs. poor speller				Addition and sequence error dominant vs. poor speller
Female vs. male	1.80	0.87		Female vs. male	1.79	0.67
Nonword reading	1.07	0.03	**	Nonword reading	1.13	0.03	***
German L2 vs. L1	0.79	0.37		German L2 vs. L1	0.51	0.20	*
Grade	1.53	0.73		Grade	6.17	2.24
Good spellers vs. poor speller				Substitution and omission error dominant vs. poor speller
Female vs. male	2.95	2.17		Female vs. male	1.91	0.59
Nonword reading	1.15	0.05	**	Nonword reading	1.08	0.02	***
German L2 vs. L1	2.20	1.70		German L2 vs. L1	0.25	0.09	***
Grade	1.48	1.03		Grade	1.91	0.58

Note. p values were adjusted using Benjamini-Hochberg corrections. OR = Odds Ratios; SE = Standard Errors of Estimations.

p < .05. **p < .01. ***p < .001.

Among secondary students, nonword decoding was still a significant predictor of the latent classifications of addition and sequence error dominant versus poor spellers (OR = 1.13; 95% CI = [1.07, 1.19]) and substitution and omission versus poor spellers (OR = 1.18; 95% CI = [1.04, 1.12]). Therefore, similar to elementary school students, secondary school students with stronger decoding skills also tended to have fewer chances of being poor spellers. German L2 was associated with a higher chance of being a poor speller (L2 on addition and sequence error dominant vs. poor speller: OR = 0.51; 95% CI = [0.12, 0.90]; L2 on substitution and omission error dominant vs. poor: OR = 0.25; 95% = [0.07, 0.43]). German L2 students were either 49% or 75% more likely to be in the poor speller latent group than the other two speller groups were. Gender was not a significant predictor for latent classification in secondary school students.

Analyses of L1 and Latent Spelling Classification

Given home language was a significant predictor of secondary school German spellers, we further examined the LCA results from the secondary school sample to examine the association of L1s and latent classifications. Table 6 shows the number and proportion of each type of speller from each L1. We then conducted posterior chi square tests to compare the proportions (proportion = number of students of each L1 in each latent classification/total number of students of that L1 × 100%). As mentioned, we focused on L1-German, L1-Turkish, L1-Polish, L1-Russian, and L1-Arabic speakers because they represented the largest student groups in the current sample. Other L1s were combined as one group. After Benjamini–Hochberg corrections, compared to German and Turkish, Polish students had significantly higher possibilities of being poor spellers (62% Polish vs. 24% German and 26% Turkish; ps < .05). Turkish students had significantly higher possibilities of being classified as addition and sequence error dominant spellers than did Arabic, German, Polish, Russian, and Turkish students (46% Polish vs. 12% Arabic, 18% German, 12% Polish, 0% Russian, ps < .05). German L1 students had higher chances of being in the substitution and omission error dominant group than did Polish and Turkish students (56% German vs. 24% Polish, 30% Turkish; ps < .05). None of the comparisons was significant in elementary school students.

Table 6.

Distribution of German Spelling Classification by L1 Orthographies and Comparison of Proportion Distributions.

Speller group	Arabic n (%)	German n (%)	Polish n (%)	Russian n (%)	Turkish n (%)	Other L1s n (%)	Chi-square comparison results using proportions
Grades 3–4
Poor	6 (35)	20 (41)	2 (33)	6 (60)	5 (46)	14 (41)	No sig. comparisons
Consonant error dominant	8 (47)	26 (53)	3 (50)	1 (30)	4 (36)	17 (50)	No sig. comparisons
Good	3 (18)	3 (6)	1 (17)	3 (10)	2 (18)	3 (9)	No sig. comparisons
Grades 5–7
Poor	12 (46)	64 (26)	13 (62)	5 (50)	12 (24)	10 (32)	Polish > German*, Polish > Turkish
Addition & sequence error dominant	3 (12)	44 (18)	3 (12)	0 (0)	23 (46)	7 (23)	Turkish > Arabic; Turkish > German*; Turkish > Polish, Turkish > Russian***
Substitution & omission error dominant	11 (42)	134 (56)	5 (24)	5 (50)	15 (30)	14 (45)	German > Polish; German > Turkish

Note. Chi-square tests were adjusted for all pairwise comparisons using Benjamini-Hochberg corrections; p values were adjusted using Benjamini-Hochberg corrections.

p < .05. **p < .01. ***p < .001.

Discussion

The current research examined German spelling profiles among students in elementary (Grades 3–4) and secondary (Grades 5–7) grades based on Treiman’s (1993) error classification method and its development (e.g., Zhang et al., 2021). Our descriptive analysis suggested that the majority of spelling errors were consonant errors. Our LCA analyses suggested three latent groups of spellers in elementary grades; namely, good spellers, consonant error dominant spellers, and poor spellers. We also found three latent groups in secondary grades; namely, addition and sequence error dominant spellers, substitution and omission dominant spellers, and poor spellers. We additionally found that although nonword decoding was a significant predictor of the latent group differences in elementary and secondary grades, home language status was a significant predictor in secondary grades only. The chi square analyses suggested Polish secondary school spellers had a significantly higher possibility of being in the poor speller latent group than did German and Turkish students. Turkish secondary students had the highest chance of being addition and sequence error dominant spellers. In the following sections, we will discuss the ways that spelling error analysis and the heterogeneity profile could inform theory and spelling instruction.

Comparing Consonant and Vowel Spelling

We found that students performed better on vowels than they did on consonant categories across the three types of spellers, because only 18% of errors in elementary grades and 28% of errors in secondary grades were vowel errors. In addition, in elementary grades, the consonant error dominant group emerged as a unique latent group, suggesting the difficulty of applying consonant knowledge in spelling for most students. Studies have suggested that in transparent orthographies such as Spanish, vowel spelling was easier to acquire than was consonant spelling, but in deep orthographies such as English, vowels posed more difficulty than did consonants (Stage & Wagner, 1992; Treiman, 1993). Researchers have suggested that German PGC was less transparent than Spanish but more transparent than English (Landerl & Reitsma, 2005; Wimmer & Landerl, 1997). Moreover, Wimmer and Landerl (1997) found that German Grade 1 students made fewer errors on initial consonant letters than they did on first vowel letters. However, our findings suggested that students in Grade 3 and above were more prone to committing consonant errors than vowel errors. Therefore, it is possible that when students face spelling tasks that are more challenging, the fact that one German consonant phoneme corresponds to many graphemes poses particular difficulties for students. Our results suggested that systematic and explicit spelling instruction might still be necessary for Grades 3 and up.

In this study, phonetic but unconventional spellings characterized the majority of consonant omission and substitution errors (e.g., omitting silent h from long vowel markers or a doubled letter, substituting a homophonic letter, or omitting t or z in tz); we suggest future researchers should study the orthographic rules associated with consonant spelling. Some orthographic rules that apply to English, such as consonant doubling at medial and ending positions (“rabbit” and “floss” rules), can also be utilized to improve German spelling proficiency (Landerl & Reitsma, 2005).

Poor Spellers

In this research, poor spellers in elementary and secondary grades made many more errors in vowel substitution (elementary n_e = 4.21; secondary n_e = 15.43) and omission (elementary n_e = 2.52; secondary n_e = 10.25) than did other classes of spellers (elementary n_e < 2; secondary n_e < 6). In the current study, vowel substitution and vowel omission errors tended to occur on multisyllabic words and long vowel markers (e.g., vowel digraphs). For multisyllabic words, training on syllable division, as suggested by Kearns and Whaley (2019), may help students attend to unstressed vowels and improve spelling. The distinction between short and long vowels also needs to be explicitly instructed to students with poor spelling profiles (Landerl, 2003).

One hundred and sixteen Grades 5 through 7 students (31%) were classified as poor spellers. Given the high number of vowel errors by these students, we assume that a significant number of them still had difficulties in preserving and differentiating vowel phonemes, especially in words with complex context (e.g., in a multisyllabic word). Therefore, differentiated instruction may need to be implemented based on individual needs despite grade level. Similarly, the poor spellers in Grades 3 and 4 made around eight vowel errors despite receiving a simpler spelling task. By contrast, good spellers in Grades 3 and 4 virtually made no vowel errors, and the consonant error dominant spellers committed around three vowel errors. It therefore is possible that these poor spellers showed difficulty patterns similar to those of students with dyslexia in other studies, such as deficiency in representing correct vowel graphemes (e.g., Landerl, 2003). Therefore, we suggest that these poor spellers have the highest risk of dyslexia and may need more focused training on vowel phoneme segmentation, identification, addition, and deletion to remediate reading and spelling difficulties. Explicit instruction on orthographic rules for short and long vowels may also help reduce vowel-spelling challenges (Ise & Schulte-Körne, 2010).

Addition and Sequence Error Dominant Spellers in Secondary School

We found that addition and sequence errors were not salient features until Grades 5 through 7. In this study, 80 students in these grades showed salient addition and sequence error patterns. These errors should not be neglected because they are typically associated with imprecise memory of the digraph patterns (adding s to the front of a ch digraph) and/or overgeneralization of spelling patterns (e.g., adding h after a short vowel). Graphotactic influence may also be associated with spelling errors due to the overgeneralization of spelling patterns (Treiman & Kessler, 2014). We therefore suggest that future studies investigate the positive and negative influences that graphotactic knowledge can exert on students. Moreover, Treiman’s (1993) original categorization did not include addition errors, but our study suggests addition errors may reflect individual differences and weakness, especially in secondary grades. Therefore, we also suggest that future studies include addition as a unique spelling error category.

Decoding and Home Language in Explaining Latent Classifications of German Spelling

Nonword decoding was a significant predictor in explaining spelling proficiency differences among all latent group comparisons. We also found that the standardized nonword scores in elementary school and secondary school students were lower than they were in other spellers. Poor spellers in elementary schools were 0.40 SD below the average, and poor spellers in secondary schools were 0.59 SD below the average. Good spellers and consonant error dominant spellers in elementary grades had nonword decoding z scores of 0.97 and 0.11, respectively. Among secondary school students, addition and sequence error dominant spellers had average z scores of 0.66 and 0.09, respectively. Poor spellers thus were the only group that had both poor spelling and below-average decoding skills. These students may need small-group interventions on decoding and spelling to reduce future literacy challenges. The poor spellers in the current study had difficulties in preserving vowel letters in a multisyllabic context and marking long vowels, which could be partially explained by the insufficient GPC skills as reflected in nonword decoding. Therefore, researchers of future studies might consider adding nonword decoding skill training for students with poor spelling profiles. Home language was not a significant predictor of latent group classifications in elementary grades, which may be explained by the few German L2 students in elementary grades. However, secondary German L2 students had a larger probability of being classified as poor spellers than German L1 students had. Although the German PGC system is more transparent than it is in English, it is less transparent than the systems of other European orthographies. Based on the orthographic depth hypothesis (Katz & Frost, 1992), the orthographic similarity between L1 and L2 may influence L2 spelling acquisition. Hence, German L2 students from transparent L1 backgrounds may find some German consonants and vowels more demanding to spell.

Polish and Turkish secondary students were more likely to be classified as poor and addition and sequence error dominant spellers, respectively, than German L1 students were. In Polish, the six vowel sounds have no long and short distinctions (Nimz & Khattab, 2019), explaining our findings that the Polish L1 students had difficulty acquiring German spelling. Turkish also does not differentiate short and long vowels except in some loan words, and Darcy and Krüger (2012) showed that Turkish L1 kindergarteners were less sensitive to German long and short vowel differences than were their German L1 counterparts. Because Turkish L1 students had a larger chance of committing addition and sequence errors than did students from other major L1s, these students might need targeted instructions on German orthographic patterns such as common consonant bigrams and vowel pairs. In addition, L1-German secondary students had a relatively low possibility of being classified as poor spellers compared to L1-Polish and L1-Turkish students. Because L1 to L2 transferring difficulties do not apply to German students, this finding suggests that German orthography tends to elicit letter omission and substitution irrespective of language proficiency. Future studies that investigate which orthographic properties have higher chances for omission and substitution errors are suggested.

Study Limitations

This study has several limitations. First, we did not include an equal number of students from various L1 backgrounds, which may explain why home language status was not a significant predictor of elementary grade students’ spelling classifications. We suggest future studies should recruit an equal number of students from various L1s and compare their spelling performance on various consonant and vowel categories. In addition, we collected the spelling data from Grades 3 through 7, but only 13 Grade 7 students agreed to participate in the study. Future studies are encouraged to recruit an equal number of students from each grade level. Moreover, we adopted a self-assessment survey to identify the L1, but future studies that administer standardized L1 literacy assessments to produce results on L1 proficiency that are more reliable are suggested. In addition, we could not collect data on our participants’ socioeconomic status, but we acknowledge that socioeconomic factors may also influence spelling proficiency. Last, this study focused primarily on differences between consonant and vowel spelling and less on the roles of phonology, orthography, graphotactic knowledge, and morphology in spelling. Future studies need to investigate how these factors interact with consonant and vowel processing in influencing student spelling accuracy.

Conclusion

The current study suggests that German students in Grades 3 through 7 have heterogeneities delineated by consonant and vowel spelling error categories. Although vowels overall were easier to spell than consonants, poor spellers in elementary and secondary grades still struggled at vowel spelling while other spellers did not. This suggests vowel and consonant spelling perhaps do not grow in tandem in some students. Secondary school students from a Polish L1 background were also found to have more difficulties attending to spelling patterns in German than did German L1 students, and Turkish L1 students had higher possibilities of committing addition and sequence errors than did other major L1s.

Current spelling theories tend to focus on English orthography in general. However, German has its unique orthographic pattern. Spelling profiles were found to be heterogeneous in this study across grades, and German L2 students may exhibit different profiles and error patterns that are influenced by L1. Given the diverse student population in German schools, attending to the unique needs of students is essential, and specific attention should be given to students who may not be familiar with the German spelling system.

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Shuai Zhang

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