One Factor SEM and Multilevel SEM Model for Patient Satisfaction Data

Structural equation models are very common in medical, social, management and behavioral sciences where researchers established some causal relations between observed variables and latent variable. In structured populations the assumption of independence of observations is often violated and had been ignored by the researchers. As a result with the correlated structure of the error terms, biased estimates of the parameters have been produced that leads towards incorrect statistical inference. Multilevel structural equation model under one factor model has been proposed, estimated and compared with the traditional structural equation model on patient satisfaction data. Multilevel structural equation model produced better estimates than the structural equation models.


INTRODUCTION
Structural equation modeling (SEM) was first developed from econometrics and then from latent variable models for factor analysis. The theory studies the causal relations between observed and latent variables. SEM is a common and useful framework for statistical analysis that covers as special cases numerous customary multivariate techniques. Structural equation models are frequently seen by a figure named path diagram [1,2]. Structural equation modeling has its origins in path analysis and it is usual to begin a SEM analysis by sketching a path diagram. A path diagram contains circles and rectangles, which are linked by arrows. Observed (or measured) variables are signified by a square box or rectangle, and latent (or unmeasured) features by a circle or ellipse. One-headed arrows or 'paths' are used to describe assumed causal associations in the model, with the variable at the tail of the arrow being the cause of the variable at the point. Statistically, the one headed arrows or paths characterize the regression coefficients [3].
As the path coefficients in a SEM model are like the regression weights in a Multiple Regression analysis which means that they control the correlations among multiple causes of the same variables. Path Coefficients represent the direct or indirect effect of an indicator or observed variable to the Latent Variable. So the violation of independence of observations in a SEM model from a structured population is pretty common. In this case, the estimates of the coefficients of a SEM model will be biased and misleading [4][5][6][7].
Behavioral, social and medical scientists often use structural equation modeling in their researches and the correlated structure of the data from a structured population must be taken into account while applying structural equation models on their data. Under clustered populations, multilevel structural equation models (MLSEM) can be used for the proper estimation of the model because MLSEM are considered the generalization of the SEM for structured populations [6,8,9].
Patient satisfaction plays a pivotal role in a consistent use of medical services in sustaining relationships with certain care-givers, and in compliance with medical rules and treatments [10][11][12][13]. Apart from that, patient or consumer satisfaction with health care services is considered to be a principal importance with regard to quality enhancement programs from the patients' perspective; total quality management and the expected consequence of care [14,15]. With this regard, studies related to patient satisfaction can be used to increase medical audit programs. However, the significance of patient satisfaction researches is also probed on the basis of theoretical and operational complications. Theoretically, most investigators consider patient satisfaction as a tool of prospects and involvements of the users of health care facilities [16,17]. Dissimilarities in patient satisfaction are due in part to patient preferences and approaches toward health care and the health care transferring practice, and in part to outdoor conditions, such as practice setting or the way health care services are systematized [18,19]. Most studies are "data driven," and concentrating on patient satisfaction scores as a regressor for subsequent performance or as the outcome variable for evaluating health care services and the behavior of health care providers. Compared with the vast amount of patient satisfaction studies that link predictor variables at the patient level to differences in patient satisfaction, the number of studies relating quality of care scores to more objective measures of service delivery or to perceived differences between care providers is relatively small [20,8].
Satisfaction of patient is greatly affected by the physician's communication with the patient [21][22][23]. In present study we apply both SEM and MLSEM models on patient satisfaction with the doctor's communication data (Table 1). Patient satisfaction measured on 13 items from 1650 patients admitted in leading hospitals of Lahore was considered level-1 units and the 14 hospitals were taken as level-2 units.  Let ij y can be written as  , ,..., j y y y is,  The two level structural equation model carries few restrictions on level-1 and level-2 components of variance.

LEVEL STRUCTURAL EQUATION MODEL
In two level SEM carry some restrictions on between ( level-2 ) and within ( level-1) variance components. By differentiating (5) w.r.t r   estimates of unknown restricted parameters was obtained.

Model Assessment and Goodness of Fit Statistics for MLSEM
In two-level structural equation model  Table 2&3 showed the estimated between hospitals covariance matrix and estimated within hospitals covariance matrix under patient's satisfaction with the doctor's communication data. Clearly we observe the differences between the two covariance matrices and comparatively the values of covariance matrix under between the hospitals model is higher than the values of within covariance matrix. Table 4 represented the results of regression coefficients, standard errors, z-statistics and p-values for the observed variables under SEM and MLSEM models respectively. Comparatively estimates under MLSEM are higher than the estimates under SEM models.

CONCLUSION
Multilevel structural equation models must be in use while studying causal relations between observed and latent variables from a clustered population even the variables of second level or higher levels are not considered in the analysis.

CONSENT
It is not applicable.

ETHICAL APPROVAL
It is not applicable.