1. Using Structural Equation Modeling in Child Language Research
Hope S. Lancaster  Stephen Camarata
Vanderbilt University School of Medicine
INTRODUCTION
EXAMPLES
discussion
Structural equation modeling (SEM) is a statistical tool that can be used to test and examine causal relationships. In SEM, manifest variables are measurable variables assumed to be representative of a larger concept called a latent construct. For example, "Language" could be considered a latent construct made up of measurable variables including standardized language assessments, language sample measures (e.g. mean length of utterance), parent report of vocabulary, etc.
SEM has been used frequently in education research, especially research on reading (e.g., Beron & Farkas, 2004; Compton, 2000; Kershaw & Schatschneider, 2012; Lervag & Hulme, 2009). However, less research in child language research has used SEM (e.g., Shriberg, Friel-Patti, Flipsen, & Roger, 2000). Applying SEM could be worthwhile because there are several benefits to the approach: for example, theory testing and information on potential causal relationships. However, unlike educational research, child language research sometimes does not have the necessary pre-requisites to use SEM (in particular, sample size). There are also constraints based on the types of measures employed in child language research. Despite the difficulties, SEM offers researchers a powerful tool that has been used successfully in related fields and can be used more extensively in child language research.
Another aspect to consider is goodness of fit. When interpreting a model using SEM, there are several statistical values to check goodness-of-fit and path coefficients. Goodness-of-fit refers to how well a model represents the underlying patterns in the data. Path coefficients estimates are analogous to beta weights in regression equations. To determine if the model had good fit various goodness-of-fit statistics were examined. The most commonly used goodness-of-fit statistic in SEM is χ2 (Cohen, 1988). It is important to bear in mind that a non-significant χ2 means that there is good fit to the data. It is advisable to use more than one goodness-of-fit statistic as different statistics provide information about different aspects of the model, such as the error in the model using Root Mean Squared Error of Approximation (RMSEA; Steiger & Lind, 1990). After determining whether a model has good fit, path estimates can be examined. When examining path estimates, a researcher is looking for a small standard error and a significant t-value (t > 1.96). Path estimates can be obtained for paths between manifest variables and latent constructs (e.g., grammar subtests to “Grammar” construct) and between two latent variables (e.g., “Grammar” to “Vocabulary”).
Structural equation modeling (SEM) can be a useful statistical tool for researchers in child language when used appropriately.
Benefits
SEM allows for the examination of constructs that cannot be directly measured. The measures that are used to build a construct can be examined to determine how well they map onto a latent construct.
Causal and associative relationships can be explored more effectively than when using regression or correlation.
Pitfalls
There is a need for multiple measures using a variety of methods of collection. It is often considered prudent to have at least three measures/methods to build a latent construct. For example, a behavioral, physiological, and parent report could be used as three manifest variables that map onto the latent construct “Stuttering.” However, this is not always feasible in a study.
To effectively model a relationship there needs to be a large sample size (e.g., N > 100).
In order to use tools, like SEM, the field needs to develop more collaborative large scale databases.
Example 1: Single latent construct
This is an example of a construct that we cannot measure directly. For this example three subtests from TOLD-P:2 are used to create a latent construct, similar to the way a composite score would be created. However, this model shows that Grammatical Completion (path = 5.09) and Sentence Imitation (path = 4.33) have more in common with the construct (“Grammar”) that Grammatical Understanding (path = 2.51). This may be the result of the expressive language component involved in both tasks.
Goodness of fit: The model is saturated (fit is perfect). Saturated models occur when there are zero degrees of freedom. Zero degrees of freedom occur when the number of paths being estimated and the number of manifest variables provided negate each other. When this occurs other measures of goodness-of-fit, such as PNFI or CFI cannot be estimated. A saturated model cannot be generalized outside of the data used to build the model.
Example 2: Latent construct predicting a manifest variable
SELECTED REFERENCES
Beron, K. J., & Farkas, G. (2004). Oral language and reading success: A structural equation modeling approach. Structural Equation Modeling, 11,
Cohen, J. (1988). Statistical power analysis for the behavioral sciences. Psychology Press.
Compton, D. L. (2000). Modeling the response of normally achieving and at-risk first grade children to word reading instruction. Annals of Dyslexia, 50,
Kershaw, S., & Schatschneider, C. (2012). A latent variable approach to the simple view of reading. Reading and Writing, 25,
Lervåg, A., & Hulme, C. (2009). Rapid automatized naming (RAN) taps a mechanism that places constraints on the development of early reading fluency. Psychological Science, 20,
Shriberg, L. D., Friel-Patti, S., Flipsen Jr, P., & Brown, R. L. (2000). Otitis Media, fluctuant hearing loss, and speech-language outcomes: A preliminary structural equation model. Journal of Speech, Language & Hearing Research, 43,
Steiger, J. H., & Lind, J. C. (1980, June). Statistically based tests for the number of factors. Paper presented at the annual meeting of the Psychometric Society, Iowa City, IA.
Tomblin, J. B., & Zhang, X. (2006). The dimensionality of language ability in school-age children. Journal of Speech, Language, and Hearing Research, 49, 1193 – 1208.
In this example, the latent construct “Grammar” is used to predict performance on a single task Word-Sound Deletion, based on the theory that developmental grammar comes before phonemic awareness. The correlation between Grammatical Understanding and Word-Sound Deletion was r = .358 (Table 1). This example provides more information about how "Grammar" might impact on Word-Sound Deletion performance, because measurement error associated with the subtests Grammatical Completion, Grammatical Understanding, and Sentence Imitation allowing for a better estimate of the relationship between "Grammar" and Word-Sound Deletion.
N.B. WSD functions both as a manifest and latent variable in this example with a path of 1.0 (a fixed path). In essence, the manifest variable WSD is exactly the same as the latent variable WSD.
Goodness of fit: χ2 (1) = 3.54 p = .059, RMSEA = [0.0 ; 0.288] p = .108, PNFI = 0.164, CFI = χ2 is non-significant, which is one sign of goodness-of-fit, however RMSEA indicates that there is missing information in the model. These goodness-of-fit values provide evidence that performance on Word-Sound Deletion can be predicted using "Grammar," but this finding is tempered with the evidence that some underlying factor in the model is not correctly specified, which is only identified when we examine goodness-of-fit beyond χ2.
METHODS
Example 3: Mediation model
Random sample of 150 TD children from EpiSLI database (Tomblin, 2010)
Table 1.
Correlations between manifest variables used in examples.
LISREL (2012) was used to test all models. All path estimates were determined using the General Least Square (GLS). Error was estimated using standard procedures (i.e., phi was set to 1 for exogenous variables and for endogenous variables one lambda path was set to 1).
Fit was estimated by examining χ2, RMSEA, PNFI, and CFI. Path estimates were examined for models with appropriate goodness-of-fit.
ACKNOWLEDGEMENTS 1 2 3 4 5 6
1. GU -
2. GC
.547
3. SI
.431
.620
4. OV
.552
.526
.535
5. PV
.386
.501
.363
.421
6. WSD
.358
.542
.541
.365
This study was supported by a Preparation of Leadership Personnel grant (H325D080075; PI: Schuele) US Department of Education.
Acknowledgement is given to original grant #N01-DC and supplement #3 P50 DC S1 from the National Institute on Deafness and Other Communication Disorders, a division of the National Institutes of Health. The authors also acknowledge support given by the Vanderbilt Kennedy Center.
The content is solely the responsibility of the authors and does not necessarily represent the views of Vanderbilt University.
Poster available at:
Notes. GU = Grammatical Understanding, GC = Grammatical Completion, SI = Sentence Imitation, OV = Oral Vocabulary, PV = Picture Vocabulary, WSD = Word-Sound Deletion
In this example, the latent construct “Vocabulary” mediates the relationship between “Grammar” and Word-Sound Deletion. “Vocabulary” was added a mediator, because in kindergarten “Grammar” and “Vocabulary” are slightly separated latent constructs in this sample (Tomblin & Zhang, 2006). Furthermore, “Vocabulary” (word knowledge) might facilitate a child's ability to complete a word based task (Word-Sound Deletion).
Goodness of fit: χ2 (6) = 42.5 p = .000, RMSEA = [0.147 ; 0.206] p = .000, PNFI = 0.367, CFI = χ2, RMSEA, PNFI both indicate poor fit with the data; however, CFI is within acceptable parameters. χ2 and RMSEA both indicate that there is underlying problem within the model, while NFI and CFI provide evidence that perhaps there are changes that need to be made to the model. For example, maybe "Grammar" and "Vocabulary" should be combined into a "Language" construct. It is inadvisable to interpret the path coefficients.