The research reported here was supported by the Institute of Education Sciences, U.S. Department of Education, through a subaward to Florida State University from Grant R305F100005 to the Educational Testing Service as part of the Reading for Understanding Initiative. The opinions expressed are those of the authors and do not represent views of the Institute, the U.S. Department of Education, the Educational Testing Service, or Florida State University.

Note: The steps below describe decomposing total variance in a dependent variable (Y) into unique variance, common variance, and unexplained variance components based on two selected independent variables (called <img alt="Equation 1" src="/files/ftp_upload/58557/58557eq1.jpg" /> and <img alt="Equation 2" src="/files/ftp_upload/58557/58557eq2.jpg" /> for this example) using software with a graphical user interface and data management software (see Table ...

<ol>
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B., Zhang, X. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=The+dimensionality+of+language+ability+in+school-age+children.">The dimensionality of language ability in school-age children.</a> Journal of Speech, Language, and Hearing Research. 49, 1193-1208 (2006).</li><li>Foorman, B., Herrera, S., Petscher, Y., Mitchell, A., Truckenmiller, A. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=The+Structure+of+Oral+Language+and+Reading+and+Their+Relation+to+Comprehension+in+grades+kindergarten+through+grade+2.">The Structure of Oral Language and Reading and Their Relation to Comprehension in grades kindergarten through grade 2.</a> Reading and Writing. 28 (5), 655-681 (2015).</li><li>Foorman, B., Koon, S., Petscher, Y., Mitchell, A., Truckenmiller, A. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Examining+General+and+Specific+Factors+in+the+Dimensionality+of+Oral+Language+and+Reading+in+4th-10th+Grades.">Examining General and Specific Factors in the Dimensionality of Oral Language and Reading in 4th-10th Grades.</a> Journal of Educational Psychology. 107 (3), 884-899 (2015).</li><li>Kieffer, M., Petscher, Y., Proctor, C. P., Silverman, R. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Is+the+whole+greater+than+the+sum+of+its+parts?+Modeling+the+contributions+of+language+comprehension+skills+to+reading+comprehension+in+the+upper+elementary+grades.">Is the whole greater than the sum of its parts? Modeling the contributions of language comprehension skills to reading comprehension in the upper elementary grades.</a> Scientific Studies of Reading. 20 (6), 436-454 (2016).</li><li>Kim, Y. S. G., Park, C., Park, Y. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Dimensions+of+discourse+level+oral+language+skills+and+their+relation+to+reading+comprehension+and+written+composition:+an+exploratory+study.">Dimensions of discourse level oral language skills and their relation to reading comprehension and written composition: an exploratory study.</a> Reading and Writing. 28, 633-654 (2015).</li><li>Foorman, B., Petscher, Y., Herrera, S. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Unique+and+common+effects+of+decoding+and+language+factors+in+predicting+reading+comprehension+in+grades+1-10.">Unique and common effects of decoding and language factors in predicting reading comprehension in grades 1-10.</a> Learning and Individual Differences. 63, 12-23 (2018).</li><li>Perfetti, C. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Reading+ability:+Lexical+quality+to+comprehension.">Reading ability: Lexical quality to comprehension.</a> Scientific Studies of Reading. 11 (4), 357-383 (2007).</li><li>Perfetti, C., Stafura, J. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Word+knowledge+in+a+theory+of+reading+comprehension.">Word knowledge in a theory of reading comprehension.</a> Scientific Studies of Reading. 18 (4), 22-37 (2014).</li><li>Torgesen, J., Wagner, R., Rashotte, C. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=.">.</a> Test of Word Reading Efficiency. , (2012).</li><li>Dunn, L., Dunn, D. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=.">.</a> Peabody Picture Vocabulary Test-4. , (2007).</li><li>MacGinitie, W., MacGinitie, R., Maria, K., Dreyer, L. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=.">.</a> Gates-MacGinitie Reading Tests. , (2000).</li><li>Wanzek, J., Wexler, J., Vaughn, S., Ciullo, S. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Reading+interventions+for+struggling+readers+in+the+upper+elementary+grades:+a+synthesis+of+20+years+of+research.">Reading interventions for struggling readers in the upper elementary grades: a synthesis of 20 years of research.</a> Reading &amp; Writing. 23, 889-912 (2010).</li><li>Foorman, B., Petscher, Y., Stanley, C., Herrera, S. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Latent+profiles+of+reading+and+language+and+their+association+with+standardized+reading+outcomes+in+kindergarten+through+tenth+grade.">Latent profiles of reading and language and their association with standardized reading outcomes in kindergarten through tenth grade.</a> Journal of Research on Educational Effectiveness. 10 (3), 619-645 (2017).</li><li>Lesaux, N. K., Kieffer, M. J., Kelley, J. G., Harris, J. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Effects+of+academic+vocabulary+instruction+for+linguistically+diverse+adolescents:+Evidence+from+a+randomized+field+trial.">Effects of academic vocabulary instruction for linguistically diverse adolescents: Evidence from a randomized field trial.</a> American Educational Research Journal. 51 (6), 1159-1194 (2014).</li><li>Lawrence, J., Crosson, A., Par&#233;-Blagoev, E., Snow, C. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Word+generation+randomized+trial:+Discussion+mediates+the+impact+of+program+treatment+on+academic+word+learning.">Word generation randomized trial: Discussion mediates the impact of program treatment on academic word learning.</a> American Educational Research Journal. 52 (4), 750-786 (2015).</li></ol>

There are three critical steps in the protocol for decomposing the variance in R into unique and common variance due to L and D. First, subtract the R2 in the L-only model from the full model to obtain the unique R2 for D. Second, subtract the R2 for the D-only model from the full model to obtain the unique R2 for L. Third, to obtain the common variance explained by L and D, subtract the sum of the two unique R2 from the R2 for the full model.
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The Simple View of Reading1 (SVR) continues as a popular model of reading because of its simplicity-reading (R) is the product of decoding (D) and language (L)-and because SVR tends to explain, on average, approximately 60% of explained variance in reading comprehension2. SVR predicts that correlations between D and R will decline over time and that correlations between L and R will increase over time. Studies generally support this prediction3,4,5. There are disagreements, however, about the functional form of SVR, with additive models (D + L = R) explaining significantly more variance in reading comprehension than product models (D &#215; L = R)6,7,8, and a combination of sum and product [R = D + L + (D &#215; L) explaining the largest amount of variance in reading comprehension3,9.
Recently the SVR model has expanded beyond regressions based on observed variables to latent variable modeling using confirmatory factory analysis and structural equation modeling. D is typically measured with untimed or timed reading of real words and/or nonwords and R is usually measured by a standardized reading test that includes literacy and informational passages followed by multiple-choice questions. L is typically measured by tests of expressive and receptive vocabulary and, especially in the primary grades, by measures of expressive and receptive syntax and listening comprehension. Most longitudinal studies report that L is unidimensional10,11,12,13. However, another longitudinal study14 reports a two-factor structure for L in the primary grades and a unidimensional structure in grades 4 and 8. Recent cross-sectional studies report that a bifactor model best fits the data and predicts R15,16,17,18. For example, Foorman et al.16 compared unidimensional, three-factor, four-factor, and bifactor models of SVR in data from students in grades 4-10 and found that a bifactor model fit best and explained 72% to 99% of the variance in R. A general L factor explained variance in all seven grades and vocabulary and syntax uniquely explained variance only in one grade each. Although the D factor was moderately correlated with L and R in all grades (0.40-0.60 and 0.47-0.74, respectively), it was not uniquely correlated with R in the presence of the general L factor.
Even though latent variable modeling has expanded SVR by shedding light on the dimensionality of L and the unique role that L plays in predicting R beyond the primary grades, no studies of SVR except one by Foorman et al.19 have partitioned the variance in reading comprehension into what is due uniquely to D and L and what is shared in common. This is a big omission in the literature. Conceptually it makes sense that D and L would share variance in predicting written language because word recognition entails the linguistic skills of phonology, semantics, and discourse at the sentence and text levels20. Similarly, linguistic comprehension must be connected to orthographic representations of phonemes, morphemes, words, sentences, and discourse if text is to be understood21. Multiplying D by L does not yield the knowledge shared by these components. Only decomposition of the variance into what is unique and what is shared by D and L in predicting R will reveal the integrated knowledge crucial to the success of educational interventions.
The one study by Foorman et al.19 that decomposed the variance of reading comprehension into what is unique and what is shared in common by D and L employed a latent variable modeling approach. The following protocol demonstrates the technique with data from students in grades 1, 7, and 10 based on single observed variables for D (timed decoding), L (receptive vocabulary), and R (standardized reading comprehension test) to make the decomposition process easy to understand. The data represent a subset of the data from Foorman et al.19.

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			<td height="21" style="height:21px;width:216px;">IBM SPSS Statistics Software</td>
			<td style="width:71px;">IBM</td>
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			<td height="21" style="height:21px;width:216px;">Microsoft Office Excel</td>
			<td style="width:71px;">Microsoft</td>
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			<td></td>
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decomposing the variance in reading comprehension to reveal the unique and common effects of language and decoding

The Simple View of Reading is a popular model of reading that claims that reading is the product of decoding and language, with each component uniquely predicting reading comprehension. Although researchers have argued whether the sum rather than the product of the components is the better predictor, no researchers have partitioned the variance explained to examine the extent to which the components share variance in predicting reading. To decompose the variance, we subtract the R2 for the language-only model from the full model to obtain the unique R2 for decoding. Second, we subtract the R2 for the decoding-only model from the full model to obtain the unique R2 for language. Third, to obtain the common variance explained by language and decoding, we subtract the sum of the two unique R2 from the R2 for the full model. The method is demonstrated in a regression approach with data from students in grades 1 (n = 372), 6 (n = 309), and 10 (n = 122) using an observed measure of language (receptive vocabulary), decoding (timed word reading), and reading comprehension (standardized test). Results reveal a relatively large amount of variance in reading comprehension explained in grade 1 by the common variance in decoding and language. By grade 10, however, it is the unique effect of language and the common effect of language and decoding that explained the majority of variance in reading comprehension. Results are discussed in the context of an expanded version of the Simple View of Reading that considers unique and shared effects of language and decoding in predicting reading comprehension.

The objective of this study was to investigate the contributions of unique and common variance of language (L) and decoding (D) to predicting reading comprehension (R) in grades 1, 7, and 10 in Florida, a state whose demographics are representative of the nation as a whole. There were two hypotheses regarding predictions of the variance explained in reading comprehension. First, after the primary grades, the unique contribution of D will significantly decrease, and the unique contribution...

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Decomposing the Variance in Reading Comprehension to Reveal the Unique and Common Effects of Language and Decoding

Here we present a protocol for decomposing the variance in reading comprehension into the unique and common effects of language and decoding.

The Simple View of Reading is a popular model of reading that claims that reading is the product of decoding and language, with each component uniquely ...

This method can help answer key questions in the social sciences field about the psychology of reading and language development. This technique illustrates how individual difference characteristics co-vary and how a unique effect may pail in comparison to an effect shared with other characteristics. The implications of this technique extend to the social sciences more broadly.As it allows accounting for the commonality of predictors that help us understand overlapping variance. To read the data into the software with a graphical user interface, click file and hover the mouse over open. Click data and locate the relevant data file on the computer.If the file type is not consistent with software with a graphical user interface, click files of type, and select the appropriate file format. Then click open. To explain the total variance based on two independent variables, click analyze and hover the mouse over regression to select linear.Click on the dependent variable in the variable list, followed by the arrow next to dependent. Click on the two independent variables in the variable list and click the arrow next to independence. Click okay and click the viewer window of the software.Use the mouse to scroll to the model summary section and record the value under R square. Then label this value total R squared. To explain the total variance based on independent variable one, repeat the total variance explanation with independent variable one only in the independent variable list and click the viewer window of the software.Then use the mouse to scroll to the model summary section, record the value under the R square column, and label this value independent variable one R squared. To explain the total variance based on independent variable two, repeat the total variance explanation with independent variable two only in the independent variable list and click the viewer window of the software. Then use the mouse to scroll to the model summary section, record the value under the R square column, and label this value independent variable two R squared.To compute the unique, common, and unexplained variance components, open the data management software, and enter the total R squared independent variable one R squared and independent variable two R squared into cells A1, B1, and C1 respectfully. Enter the total R squared value into A2.The independent variable one R squared value into B2, and the independent variable two R squared value into C2.To calculate the unique variance of variable one, enter the formula into D2, and label this value as unique variance of variable one in D1.To calculate the unique variance of variable two, enter the formula into E2, and label the value as unique variance of variable two in E1.To calculate the common variance between variables one and two, enter the formula into F2, and label this value as common various between variables one and two in F1.To calculate the unexplained variance, enter the formula into G2, and label this value unexplained variance in G1.To plot the unique variance of variable one, the unique variance of variable two, the common variance between variables one and two, and the unexplained variance, click and drag the mouse cells over D2, E2, F2, and G2 to highlight the data, and click insert, then click charts, pie chart, and 2D pie chart. In this representative study of unique and common variances of language and decoding for predicting reading comprehension, the regression analysis for grade one students accounted for 60%of the total variance in reading comprehension.When the variance in grade one was decomposed into unique and common effects, decoding uniquely explained the 24%of variance in reading comprehension, and language uniquely explained the 17%of variance. The common variance of decoding and language was 19%In grade seven, the regression analysis accounted for 53%of the total variance in reading comprehension. With decoding uniquely explained by 7%of the variance in reading comprehension, and language explained 28%of the variance.The common variance of decoding and language in explaining the variance in reading comprehension was 18%In grade 10, the regression analysis accounted for 61%of the total variance in reading comprehension. With decoding uniquely accounting for a 6%of the variance, and language uniquely accounting for 42%of the variance. The common variance of decoding and language in explaining the variance in reading comprehension was 13%While attempting this procedure, it's important to remember that the decomposition process differs from typical regression approaches of separately calculating the unique variance that each independent variable explains.This protocol can be modified to answer additional questions about whether the proportions of unique and common variances differ by socioeconomic status. Further, the observable variables can be replaced with latent variables to reduce measurement error. The amount of common variance that decoding and language together explain in predicting reading comprehension, especially in the elementary grades suggest that instruction should focus on the integration of linguistic knowledge at the word level.

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6.6K visualizações.  Florida State University. Esse método pode ajudar a responder a perguntas-chave no campo das ciências sociais sobre a psicologia da leitura e do desenvolvimento da linguagem. Esta técnica ilustra como as características da diferença individual co-variam e como um efeito único pode se enrosco em comparação com um efeito compartilhado com outras características. As implicações dessa técnica se estendem mais amplamente às ciências sociais.Como permite contabilizar a comunhão dos preditores que nos a...