Using Tinto's model of institutional departure, longitudinal data drawn from sophomore and senior cohorts in the High School and Beyond study (HS&B), and a variation of the statistical technique known as structural equation modeling, the present study sought to call attention to certain theoretical and methodological issues that arise when studying American Indian and Alaska Native (AI/AN) postsecondary departure. A variation of structural equation modeling that treats all constructs as observed variables was used because of the small sample size. An initial confirmatory analysis found a weak fit between the Tinto model and the AI/AN sophomore cohort data. However, during an exploratory analysis minor revisions to the model suggest that family background, postsecondary intentions (both prior to and during college), and formal and informal academic integration are the most significant aspects in Tinto's model that influence AI/AN postsecondary outcomes. In addition, important aspects of the Tinto model for the sophomore cohort only included the effects of academic skills, personal abilities, and prior schooling on initial postsecondary intentions. A confirmatory analysis using AI/AN senior cohort data found that initial postsecondary intentions and goal commitment are important factors that influence academic integration. These findings support existing research calling for more programs that foster positive family support and postsecondary intentions early in an AI/AN student's high school experience. Further, it was stressed that support programs should be in place to enhance academic and social integration while A1/ANs are in college. Finally, it was recommended that the sample size of AI/ANs in national data bases like HS&B need to be increased and the indicators need to be improved so that in the future better research can be conducted on American Indian and Alaska Native postsecondary outcomes.

This article illustrates one way to examine American Indian and Alaska Native (AI/AN) postsecondary departure using: an existing mainstream model, national longitudinal data base, and a variation of the statistical technique known as structural equation modeling. A multitude of studies have assessed Tinto's (1975, 1987) model of institutional departure using data gathered from a variety of ethnic and racial student populations and different types of institutions. Nevertheless, studies that examine the validity of Tinto's model exclusively with AI/AN data are nonexistent; an objective of the present study is to fill this void. Moreover, studies that report on AI/AN data in existing national longitudinal data bases are uncommon in the field of higher education research. While addressing this concern, the second objective of the present study is to explore the strengths and weaknesses of using AI/AN data in one particular data base. Finally, a popular statistical technique for assessing the validity of an existing model with empirical data is structural equation modeling. Published studies that use structural equation modeling to examine AI/AN postsecondary departure are rare; the third objective of the present study is to introduce basic elements of structural equation modeling and discuss how the statistical results can be used to clarify implications for theory, practice, and future research.

The continuing need among Native researchers and others to enhance future research on AI/ANs in higher education provided the impetus for assessing the validity of an existing mainstream model with AI/AN data and for discussing methodological issues related to the use of national longitudinal data bases. Although problematic at this early stage, we offer the present article as one means of contributing to the dialogue. The first section presents the research questions. The second section sets the conditions for selecting a mainstream model to explore AI/AN postsecondary departure and places the model within the context of recent literature. The third section explains the rationale for selecting an existing data base and the statistical procedures used in the analysis. The fourth section presents the findings. The fifth section describes the theoretical, practical, and future research implications of the study.

The purpose of this study was to assess the extent to which Tinto's model applies to a sample of AI/AN students. There were two specific research questions:

1. Using structural equation modeling, how well does the Tinto model account for AI/AN postsecondary departure?
   
2. If the model is rejected as presently stated, can the model be modified to make it more applicable to AI/ANs?
   

The body of literature that examines the factors which influence AI/AN attrition prior to degree completion is expanding. Researchers have the choice to either develop new conceptual frameworks or to use existing models to explore these issues further. Both approaches have value. The present study illustrates the latter approach of using an existing model. In this section, we discuss the rationale for selecting a mainstream model to guide research concerning AI/ANs, compare the model to published studies, and explain why it is necessary to assess the validity of a mainstream model with AI/AN data.

Choosing a mainstream model. Relying upon the literature to find a conceptual framework is a common practice in educational research. The practice of choosing an existing framework indicates not only a familiarity with the research literature but also recognizes the value of previous scholarship. It is often useful in newer areas of study to draw upon more extensive research done elsewhere to identify possible factors that are pertinent to the phenomenon under study. For example, few studies have advanced a longitudinal model that describes the factors influencing college outcomes such as departure or persistence among AI/ANs. On the other hand, the higher education research literature on college students contributes several popular models that attempt to explain the factors that influence college outcomes (for a review of studies, see Kuh, Bean, Bradley, Coomes, & Hunter, 1986; Pascarella & Terenzini, 1991). We chose one of the most popular of these models and compared it to the literature on AI/AN postsecondary departure/persistence.

The model chosen is the well-known Tinto model of institutional departure. Building on the work of Spady (1970), Tinto presented a model of postsecondary attrition that has had widespread influence on research literature which examines various student and institutional factors related to postsecondary outcomes like departure. Briefly, Tinto postulates that a student's pre-entry attributes (i.e., family background, skills and abilities, and prior schooling) affect his or her postsecondary intentions, goals, and commitments prior to entering a higher education institution. Departure prior to degree completion occurs when there is an incongruency between the student's pre-entry attributes, intentions, goals, and commitments and the campus environment. This incongruency becomes evident during the student's integration into the formal and informal academic and social systems of the institution. Thus, the experience of integrating into these systems becomes a new influence on the student's postsecondary intentions, goals, and commitments to persist or depart.

Comparing the Tinto model to research literature on AI/ANs. A review of the literature on AI/ANs in higher education would seem to support various aspects of the Tinto model. For example, some researchers have found that preentry attributes like family background (Osborne & Cranney, 1985; Rindone, 1988), academic skills and personal abilities (Artichoker & Palmer, 1969; Wittaker, 1986), and prior schooling (Baty & Chiste, 1986; Lin, 1990) correlate with AI/AN student postsecondary outcomes. Other studies indicate that AI/AN students with postsecondary intentions, goal commitments, and institutional commitments developed in high school are more likely to persist in college (NCES, 1988a, 1988b). Moreover, intentions and commitments while in college significantly influence how willing AI/AN students are to integrate into the campus environment (Edwards, Edwards, Daines, & Reed, 1984). The degree of integration may depend on the available institutional support systems, and if certain support systems are not in place or the degree of satisfaction in using the support services is not high, then it is likely that the institutional experience will lessen goals and commitments which then lead to departure (Falk & Aitken, 1984; Lin, LaCounte, & Eder, 1988; Wells, 1989; Wright, 1985).

The necessity for assessing the Tinto model with AI/AN data. Although the literature on AI/AN college students is generally supportive of the Tinto's model, no single study has examined the longitudinal process of AI/AN postsecondary departure as presented in the model. Yet, some researchers believe that postsecondary education attrition rates among ethnic and racial minorities are insufficiently explained from established mainstream social perspectives (Ogbu, 1978, 1987; Trueba, 1988). More specifically, the postsecondary persistence and attrition (or student development) literature focusing on AI/ANs (Johnson & Lashley, 1988; LaCounte, 1987), Asians (Sue & Sue, 1971; Chew & Ogi, 1987), African Americans (Bowser, 1981; McEwen, Roper, Bryant, & Langa, 1990) and Hispanics (Martinez, 1988; Olivas, 1983, 1986) suggests that mainstream perspectives may inadequately explain minority college student experiences. Therefore, prior to using models like Tinto's to explain A1/AN postsecondary attrition it is necessary to assess them with AI/AN data.

Besides assessing a mainstream model with AI/AN data, another objective of the present study is to underscore the importance of analyzing AI/AN data in national longitudinal data bases. For example, despite the many studies based on longitudinal surveys sponsored by NCES (see for example NCES, 1985) few report findings on AI/ANs. Because the sample size was small and the self-identification unreliable, student research which uses longitudinal data has a tendency to neglect AI/AN students (Tippeconnic, 1990). Nevertheless, findings which use national longitudinal AI/AN data are occasionally reported in the literature (NCES, 1988a, 1998b; Swisher & Hoisch, 1992; Swisher, Hoisch, & Pavel, 1991) because they appear to be the "best" data available. Along with continued lobbying, one strategy to improve sampling procedures and measurement in future national longitudinal studies sponsored by NCES is for AI/AN scholars to analyze the AI/AN data in these data bases and make appropriate recommendations in published studies. The intent of such published research is to establish a continued presence and interest among a cadre of Native scholars who analyze AI/AN data in NCES data bases and call attention to issues like sampling and measurement. In addition to calling attention to these issues, this section illustrates various strategies that the analyst can use when confronting various predicaments associated with a small sample in a national data base.

Data base and sample. The HS&B data base contains longitudinal survey data collected from a sophomore and senior cohort from 1980 to 1986. The base year survey employed a two-stage, highly stratified cluster sample design with schools as the first stage units and students within schools as the second stage units. Three subsequent follow-up surveys, administered in 1982, 1984 and 1986, retained the multi-stage, stratified, clustered design of the base year survey. For complete details concerning the HS&B data collection and management procedures, see Contractor Report: High School and Beyond 1980 Senior and Sophomore Cohort, Third Follow-up, Volumes I and 11 (NCES, 1987a, 1987b).

The AI/AN sample in HS&B consists of a relatively small sample size of 351 sophomores and 229 seniors. Self-identification was verified for many of the respondents by comparing student files with data collected on parent backgrounds. The sample size was reduced, however, due to the lack of postsecondary participation for some respondents (particularly among the sophomore cohort) and a large number of missing values in individual records. To offset the impact of missing data, we evaluated the extent of missing data in each AI/AN record or case to determine which ones could be "repaired" by estimating values for missing data, a process often referred to as imputation. If almost all variables on a record had missing values, then it was deleted from the data set. On the other hand, if a marginal number of variables had missing values, an imputation procedure was used to obtain values for the missing data. Fifteen cases from the sophomore cohort and 16 cases for the senior cohort in the data set were retained during this procedure (for a helpful review of imputation procedures, see Little & Rubin, 1990). The total sample used in the analysis included 197 sophomore and 191 senior AI/AN cohort cases.

Data. Survey items relevant to this study pertain to individual and family background, cognitive test results measuring verbal and quantitative abilities, and high school experiences. Additional data were collected on the subjects' educational and occupational intentions as well as commitments in high school, postsecondary experiences, and educational/occupational intentions after being in college. Finally, 4 years later for the sophomore cohort and 6 years later for the senior cohort, data were collected on their educational attainment after graduating from high school. Table 1 lists survey items relevant to this study by the year of survey and construct, sophomore and senior HS&B variable label, indicator intended to measure, and measurement scale.

Analysis. Structural equation modeling was chosen as the quantitative technique to assess Tinto's model, in part, to meet the present study's third objective. Over the last decade, structural equation modeling has become quite popular in social science and education research. We found that few studies have applied this statistical technique to examine the complex phenomena of AI/AN students going to college. Equally as important, though, structural equation modeling was chosen over other quantitative assessment techniques—like traditional path analysis and multiple regression models—because such techniques were considered too restrictive. For example, path analysis assumes:

1. That relationships among variables are linear, additive, and causal;
   
2. The error terms in equations are not correlated;
   
3. The relationship among the variables is recursive and unidirectional;
   
4. The variables are measured on at least an interval scale;
   
5. The variables are measured without error.
   

Survey Year and Construct/Variable	Soph. Cohort Variable Level Measurement	Senior Cohort Variable Level	Indicator	Measurement
1980 and 1982
Family Background	FUSESQ FY63A FY63B	BYSESQ BB050A BB050B	Socioeconomic status Father's influence on post H.S. plans Mother's influence on post H.S. plans	1 =lowest to 4=highest 1=no college to 4=college degree* 1 =no college to 4=college degree*
Skills and Abilities	FUTESTQ FECONCPT FELOCUS	BYTESTQ FECONCPT FELOCUS	Math and language abilities Self-concept measurement Locus of control measurement	Quartile distribution of test scores Quartile distribution of composite scores Quartile distribution of composite scores
Prior Schooling	HSGRADES HSPROG	HSGRADES HSPROG	Self-reported high school grades High school program	1=F to 8=A* 1=vocational to 3=academic
Intentions-TI	FY80 FY77A	BB065 BB7062A	Postsecondary aspirations Occupational aspirations	1 =no college to 3=graduate degree* 1=requires no college degree to 3=requires advanced degree*
Goal Commitment-T I	FY83	BB069	Self-reported ability to finish college	1 =definitely not to 5=definitely yes
Institutional Commitment-TI	FY82	BB067	Lowest level of education satisfied with 1 =no high school degree to 5=professional degree*
1984 and 1986
Formal Academic Integration	TY28D SY22 TY28A	FE40V FE41 FE40A	Satisfaction with intellectual growth Self-reported postsecondary GPA Satisfaction with ability of teachers	1=not very satisfied to 5=very satisfied 1=F to 8=A* 1 =not very satisfied to 5=very satisfied
Informal Academic Integration	TY28J TY28F TY28H	FE40J FE40F FE40H	Satisfaction with quality of instruction Satisfaction with buildings, library, etc. Satisfaction with intellectual life	1=not very satisfied to 5=very satisfied 1 =not very satisfied to 5=very satisfied 1 =not very satisfied to 5=very satisfied
Formal Social Integration	TY28K	FE40K	Satisfaction with sports and recreation	1 =not very satisfied to 5=very satisfied
Informal Social Integration	TY28G TY28B	FE40G FE40B	Satisfaction with cultural activities Satisfaction with social life	1=not very satisfied to 5=very satisfied 1=not very satisfied to 5=very satisfied
Intentions-T2	TY19A TY15A	FE12 FE16A	Postsecondary aspirations Occupational aspirations	1=no college to 3=graduated degree* 1=requires no college degree to 3=requires advanced degree*
Goal Commitment-T2	PSEPLANS	PSEPLANS	Self-reported ability to finish college	1=definitely not to 5=definitely yes
Institutional Commitment-T2	TY28M	FE40M	Satisfied with prestige of school	1=not very satisfied to 5=very satisfied
1986
Outcome	EDATTAIN	EDATTAIN	Educational attainment by 1986	1=no college degree, 2=college degree*

*Recoded


At least two of these assumptions could not be met in the present study. Namely, not all of the variables are measured on at least an interval scale in NCES surveys, and the error among variables may not be uncorrelated. Likewise, other assumptions underlying the Tinto model may be inappropriate for multiple regression models that assume variables have a normal distribution.

Commercially available computer programs like LISREL and LISCOMP have made structural equation modeling accessible to researchers with at least an intermediate understanding of the mathematical concepts. These computer programs are flexible in terms of specifying which structural coefficients, used to measure the hypothesized relationship between two variables, are to be estimated and which will be assigned set values. This flexibility allows the analyst to confront a wide variety of problems when trying to assess the fit between a model and empirical data. Structural equation modeling, with or without these computer programs, does not have greater power for making inferences regarding "causality" than any other correlational analysis. However, structural equation modeling which uses computer programs has greatly reduced the complexity of specifying these relationships with non-experimental data and takes into account direct and indirect effects plus error (Bender, 1984). There are primers that provide a general overview of its application (Baldwin, 1989; Byrne, 1989; Moline, 1988), intermediate presentations involving topics related to theory and the mathematical concepts (Carmines & McIver, 198 1; Long, 1983a, 1983b), as well as more advanced discussions (Bollen, 1989; Hayduk, 1987). Here, we provide a general introduction to the terminology and basic features of structural equation modeling.

Structural equation modeling involves an analysis of covariances among observed variables to assess the hypothesized relationships among constructs within a theoretical model. Some of the most basic assumptions in assessing an existing model which uses structural equation modeling are: (1) the substantive theory is grounded in sound research, and (2) the sample size is larger than the number of structural coefficients, or hypothesized relationships, to be estimated. Using Tinto's model would appear to satisfy the first assumption. Satisfying the second assumption requires that the analyst determine precisely how the structural equation modeling process is to be carried out.

The analyst can employ structural equation modeling in a variety of ways, but generally a structural equation model and two measurement equation models are applied. Computing the structural equation model uses matrix algebra, with various terms representing matrices or vectors in the linear structural equation.

One of the first tasks that an analyst must confront is to determine the number of structural coefficients to be estimated in order to determine if the model can be identified. The identification problem has to do with seeking a solution where there are unique values for estimates of structural coefficients. When a structural coefficient cannot be assigned a unique value, a situation exists where any selection of an acceptable value is arbitrary because it is dictated by neither theory nor data. Identification may depend on the amount of information available in the data compared to the number of structural coefficients to be estimated. In other words, the sample size must be sufficient to enhance the numerical stability for each structural coefficient to be estimated in the structural equation model as well as the two measurement equation models. While the Tinto model could be theoretically identified during a pilot study, the sample size in this application proved insufficient to the task of practical estimation. In such case, the analyst may be required to reduce the number of structural coefficients to be estimated or add more data.

This study cannot add more data or increase the sample size because it uses an existing data base. As shown in Figure 1, to reduce the number of structural coefficients to be identified, the measurement models were forsaken and all latent variables treated as observed x- and y-variables. Each variable is measured by a single survey item or an amalgamation of two or more survey items. A drawback of following such a procedure is that the analyst must assume that the observed variables are measured without error and are adequate indicators of the latent variables in a model. Source: Tinto (1987), pg 114.

Nothing changes about Tinto's model when treating all the latent variables (or constructs) as observed variables only. Fortunately, reducing the number of coefficients increases the numeric stability during estimation and results in identification. The variation and covariation among postsecondary outcomes are to be accounted for by the x-variables and other y-variables with the understanding that it represents a causal structure underlying the covariation in a set of variables and their relationships (Joreskog & Sorbom, 1989b). This is expressed as noted earlier, LISREL and LISCOMP are computer programs on the market that carry out the structural equation modeling analysis. However, each has particular strengths and weaknesses. LISREL is a more refined program, easier to use, and offers better statistical output to assess theoretical models with interval data, and is also used in tandem with PRELIS for categorical non-normal data. On the other hand, LISCOMP is specifically designed for studies using categorical nonnormal data (Ethington, 1987; Muthen, 1984; Stage, 1988). We chose to use LISREL in the exploratory phases of the analysis and LISCOMP for the confirmatory phases of the analysis. Only the LISCOMP results are reported in this article.

Both LISREL and LISCOMP programs generate statistics for assessing a theoretical model with quantitative data. The statistics reported here are component fit measures and overall fit measures. Component fit measures include standardized coefficient estimates-calculated with a covariance matrix so that values may exceed 1.0—and standard errors used to assess strengths and weaknesses of various components within the model. Using traditional hypothesis testing procedures, coefficients twice as large as their standard errors are considered significant with alpha set at .05. Coefficients less than twice as large as their standard errors are considered insignificant because they may be due to sampling fluctuations and not to real effects.

The root mean square residual (RMR), chi-square statistic (X2) [2 is superscripted in original document] with associated degrees of freedom (df), and probability level (p) can be used to determine the model's overall fit to the empirical data. The RMR is an average of the error variances and covariances among the various relationships depicted in the model and is used to assess incremental changes to the model using the same data by taking the average discrepancy between structural coefficient estimates and hypothesized covariance matrices. The RMR is measured on a scale of 0 to 1.00 and values <.05 are preferred.

The X2/df ratio and associated p level are used to evaluate the model's overall fit to the data. A high ratio of X2 to df with p <.05 will indicate a poor fit between the model and the data. A low ratio with p >.05 indicates a good fit. Depending on sample size, acceptable values for the X2/df ratio range from <2.00 (Byrne, 1989) to <3.00 (Carmines & McIver, 1981), with <5.00 sometimes considered a reasonable starting point to consider additional refinements (Wheaton, Muthen, Armin, & Summers, 1977).

A small X2 with p>.05 indicates a close correspondence between the theory and sample data (Carmines & McIver, 1981). The effect of sample size on the X2 statistic is well known even when incorporating degrees of freedom (Marsh, Balla, & McDonald, 1988). On the other hand, simulated studies appear to suggest that the X2 test is supported as a valid assessment of model fit with sample sizes approaching 200 (Boomsma, 1982).

The component fit measures and measure of overall fit need to be interpreted collectively and cautiously if the model is complex and the sample size is relative small (Anderson & Gerbing, 1988; Bollen, 1989; Gallini & Mandeville, 1984; Schmitt & Bedeian, 1982). As in the case of this study, the sample size is considered small when it has between 10 to 20 cases per variable. Optimally, a rule of thumb is that a study of this nature should strive to have at least 40 cases per variable or five to ten cases per parameter or structural coefficient to be estimated.

If the model is rejected, LISREL provides output not available from LISCOMP (e.g., modification indices, stem and leaf plots, and a QPLOT) that helps the analyst explore how the model could be improved to produce a better fit with the empirical data and to assess the significance of those modifications. Any changes made during an exploratory mode, in terms of deleting or adding paths from and to certain variables, should be consistent with the theoretical model. Modifications to a weak model are made individually, and in a stepwise fashion, so that results of the new model can be compared to the previous version(s) of the original model. Once an acceptable model has been fitted to the data (i.e., modified to better reflect the sample data), the analysis should be replicated (or the model confirmed) with another sample. As presented in the next section, the study initially assessed the Tinto model with the HS&B sophomore cohort and replicated the study with the senior cohort.

Initial assessment. In accordance with the first research question, an initial assessment of Tinto's model (as shown in Figure 1) resulted in the determination that there was a weak fit between the model and the Al/AN HS&B sophomore cohort data; the X2/df ratio of 9.0, p >.000, and RMR=.28 were deemed unacceptable and the component fit measures unreliable. This means that the analyst should reject the model—in its present state—as not being representative of the sample data. The analysis could end at this point. However, to address the second research question, we chose (as is common in this type of research) to execute an exploratory procedure to see if theoretically consistent and reasonable modifications could better fit the Tinto model to the AI/AN sophomore cohort data. In other words, to determine how the model could better represent the sample data by deleting and/or adding paths.

Fitting the Tinto model to the data. The Tinto model was fitted to the sophomore cohort data by adding or deleting paths until the measures of overall fit (X2/df ratio=1.05, p=.39, and RMR=.06) were within or near the limits established in this study as being acceptable. During this phase, all paths added during the exploratory analysis were statistically significant at the .05 alpha level and consistent with the theoretical model (see Note 1). This means that paths were added when: (1) each coefficient (or path in the model showing a relationship) to be estimated was significantly different from zero while improving the overall fit of the model to the sample data, and (2) the paths were reasonable given the views advanced by Tinto.

Figure 2 shows the fitted Tinto model in path diagram form; it identifies paths that were significant in the initial Tinto model as well as the significant paths that were added during the exploratory mode. Although retained throughout the analysis, all paths not statistically significant included in the initial assessment of the Tinto model shown in Figure I are absent in the remaining figures to reduce clutter. Collectively, all the paths (whether statistically significant or not) help to account for approximately 40% of the explained variance in postsecondary outcomes.

During this stage of the exploratory analysis it is important to address the issue of whether or not the significant path coefficients make sense. Although several unusual relationships (paths) could have been kept from the fitted model, we decided to leave them in for discussion purposes. For example, though the effect is small, it seems that significant negative effects of Prior Schooling on Outcome are contradictory to what one might expect. For example, a positive relationship would mean that those respondents with a high grade point average and pursuing an academically oriented program of study in high school are more likely to get a degree than those who had a low grade point average and pursued a general program of study. A cross tabulation of Prior Schooling by Outcome revealed that 42% or 17 out of 40 respondents having the lowest values measuring Prior Schooling (i.e., low grade point average and pursued a vocational program of study in high school) received a postsecondary degree compared to only 26% or 9 of the 34 who had the highest values (i.e., high grade point average and pursued an academic program of study in high school). Later, we will touch on the ramifications of these findings while discussing implications for future research.

Confirming the fitted Tinto model. The next step in the analysis was to replicate or conduct a confirmatory analysis of the fitted Tinto model with AI/AN HS&B senior cohort data. During this phase, no attempt was made to modify the model but rather confirm that the modifications made on the bases of the sophomore cohort data were sound. The confirmatory analysis also resulted in an acceptable X2/df ratio (1.11), probability level (.30), and RMR (.06) to at least indicate that the modified model adequately accounts for AI/AN postsecondary outcomes. Figure 3 is a path diagram showing the significant paths of the fitted Tinto model with the senior cohort data.

Again, there were several significant coefficients that deserve closer inspection. The small but negative effect of Institutional Commitment-T2 [2 is subscripted in original document] on Outcome appears contradictory to what one might expect. For example, students with a higher degree of satisfaction with the campus social life and cultural activities would be expected to develop a goal commitment to complete college. Likewise, those most satisfied with the prestige of a school are more likely to acquire a postsecondary degree than those who are not as satisfied. A cross tabulation of Informal Social Integration by Goal Commitment-T2, revealed that 47 of the 191 respondents had high measures of Informal Social Integration with high measures of Goal Commitment-T2. However, 51 respondents had high measures of Informal Social Integration with low measures of Goal Commitment-T2. A cross tabulation of Institutional Commitment-T2, by Outcome indicated that out of 108 respondents with high measures of Institutional Commitment-T2, over half did not receive a postsecondary degree 6 years after high school graduation, suggesting that students attending what they consider to be prestigious institutions are not graduating. We also address the ramifications of these findings while discussing implications for future research.

There are several caveats which need to be acknowledged prior to discussing the implications of these findings for theory, practice, and future research. Namely, the small AI/AN sample drawn from HS&B poses some difficulties in rigorously assessing the applicability of Tinto's model to AI/AN students. As already noted, self-identification is a suspect measure, and the small sample size required the elimination of the measurement models while assuming that the indicators were measured without error. Clearly, a more rigorous research design is needed to attend to these issues. Acknowledging these limitations, what follows is a discussion of the theoretical, practical, and future research implications of the fitted Tinto model.

Theoretical implications. The statistically significant coefficients when applied to AI/AN data can help guide a discussion of the implications for Tinto's model. For both sophomore and senior cohorts, the most important variables/constructs that directly and indirectly affect postsecondary outcomes include family background, postsecondary intentions, and academic integration. Among the pre-entry attributes, family background had the largest and most consistent influence on postsecondary intentions prior to pursuing a postsecondary degree. In turn, postsecondary intentions after being in college and formal academic integration consistently had an influence on postsecondary outcome while informal academic integration had an indirect influence on outcomes through formal academic integration for both cohorts.

The findings also suggest variations in the sophomore and senior cohorts. In the context of the sophomore data only, other important factors include academic skills, personal abilities, and prior schooling on initial postsecondary intentions. In addition, academic integration directly influences informal social integration that, in turn, directly influences outcome. Informal academic integration also directly influences outcome. For seniors only, the effects of initial goal commitment on formal academic integration and initial postsecondary intentions on informal academic integration are significant. The significant effect of formal academic integration on outcome is also apparent through its direct influence on postsecondary intentions while pursuing a postsecondary degree that, in turn, significantly influences outcome.

The results indicate that some aspects of the Tinto model are more salient than others when applied to AI/ANs. Because the fit is far from perfect, however, it is likely there are factors outside the model that are also influencing postsecondary outcomes. These factors may be associated with policy environments and organizational characteristics (Richardson & Skinner, 1991), financial aid (Cabrera, Stampen, & Hansen, 1990), or external commitments (Tinto, 1987). However, it is unclear to what extent these and other factors might influence AI/AN postsecondary outcomes because no proper indicators for these factors were available in the HS&B data base, and generally they have not been included in other published research using the Tinto model.

Implications for practice. It is usually informative for the analyst to compare research findings with the available published literature before advancing recommendations for practice. Moreover, in statistical studies of this nature, the size of the coefficients should help in determining where program resources may be directed (i.e., higher statistically significant coefficients indicate areas that should be given attention). Overall, the majority of factors within the Tinto model that had a statistically significant effect on postsecondary outcome for both cohorts support the findings of other studies, and thus give some credibility to the present study. For example, as other research has shown, institutional efforts to recruit AI/AN students could emphasize the need to reach out to the parents and encourage the development of postsecondary intentions (Edwards et al., 1988; Lin, 1990; Osborne & Cranney, 1985; Rindone, 1988). College orientation activities on reservations and urban Indian centers are effective outreach activities. Informative and culturally appealing materials can be made available to help parents plan for the day when their children may go to college. Counselors in high school can assist students prior to and during their pursuit of a postsecondary degree to maintain their postsecondary intentions (Bransford, 1982; Kleinfeld, Cooper, & Kyle, 1987).

The findings also support studies by Wilson (1983), Wittaker (1986), and Eberhard (1989), suggesting that high schools should help AI/AN students to acquire the academic skills and personal abilities that will allow them to cope with the rigors of pursuing a postsecondary degree. As implied by the sophomore cohort results and pointed out by Newell and Tyon (1989), program directed at developing skills and abilities should reach AI/AN students early in their high school experience rather than later. This means encouraging AI/AN students to participate in college preparatory classes or develop study skills while they are sophomores rather than tracking them into predominantly vocational or general programs of study.

The statistically significant effects of academic integration on postsecondary intentions speak to the need that academic support services should be in place to positively influence AI/AN degree attainment. Consistent with Falk's and Aitken's (1984) study, institutional outreach that develops family support and provides sufficient college orientation also needs to include aggressive retention programs. Efforts to promote academic integration of AI/AN students could include informal faculty/student activities that lead to positive interaction inside and outside the classroom (Erickson, 1986; Erickson & Shultz, 1982; Lin, LaCounte, & Eder, 1988; Scollen, 1981). In addition, required first year orientation activities could instruct students on how to locate and use various academic resources and cultivate student support networks on campus in order to improve classroom performance (McNamara, 1981; Wells, 1989). As called for by Guyette and Heth (1984), Fallows (1987), and Kleinfeld (1987), it may be necessary to hire a critical mass of faculty role models who could assist AI/AN students to adjust to the demands of college. In addition, it is important that academic advisors and faculty understand the stress related factors that AI/AN students encounter (Padilla & Pavel, 1991; Skye, Christensen, & England, 1989).

Problems associated with college academic life and postsecondary outcome are complicated by a lack of positive social integration experiences. Support programs that ameliorate home sickness and that buffer the transition from the social environment of the high school to the collegiate social environment are needed. As others have indicated, promoting ethnic studies and pride (Kirk, 1989; Scott, 1986; Wright, 1985), ethnic student enclaves (Murguia, Padilla, & Pavel, 1991), and culturally appropriate activities (Bennett, 1990; Huffman, Sill, & Brokenleg, 1986; Jeanotte, 1980; Swisher & Deyhle, 1987) help students cope with the educational environment, and achieve an ego-centered locus-of-control and a positive self-concept so important in maintaining the motivation to finish college. Collectively, these factors play an important role in enhancing the institutional experience of Al/AN students who seek to complete a degree program.

Implications for future research. Although discussed at length elsewhere (Pavel & Reiser, 1991), at least three issues should be addressed to improve future research using NCES data bases to examine AI/AN postsecondary departure. The first issue involves increasing the AI/AN sample. Two closely related issues are unproved self-identification and inclusion of better indicators in the data base relevant to AI/AN students.

The sample size of AI/ANs must be increased in NCES studies if we are to extend our thinking about the complex web of factors that influence AI/ANs to either flounder or succeed in America's higher education system. Such issues can be investigated properly only with samples of appropriate size and inclusivity. To address this sampling issue, NCES should make a special effort to compile pile data bases with a sufficient sample of AI/ANs (e.g., say at least 2000 to 3000 respondents) so that more insightful research can be conducted across regions, various tribal groups, and within and between institution types. NCES or their contractors could increase the AI/AN sample size by concentrating sampling in the 10 states that have around 60% of the AI/AN populations (Hodgkinson, Outtz, & Obarakpor, 1990). Moreover, schools with high concentrations of AI/AN students should be targeted as the first unit of analysis. It should be noted that previous attempts to include Bureau of Indian Affairs schools have been unsuccessful, and the present number of AI/AN respondents could be attributed to repeated efforts to over sample Hispanics.

A closely related issue to sampling is self-identification. The gross category of "American Indian and Alaska Native" needs to be followed by more precise measures that may include tribal affiliation, degree of ancestry, and tribal enrollment status. Also of concern is the need to explore linkages to Native communities that might distinguish respondents from more traditional backgrounds or those maintaining their cultural heritage in urban settings who face additional obstacles while growing up. Although such survey items are not a panacea for better identifying "Indians" who have been historically underrepresented in mainstream higher education, such items are needed to better distinguish AI/ANs respondents from those who simply want to identify as AI/ANs because of some romantic or other misconceived notion.

Another issue is the selection and adequacy of HS&B survey items to serve as indicators of constructs in Tinto's model. For example, the negative coefficients found in this study which link prior schooling and institutional commitment to postsecondary outcome appear unusual. Although these paths only marginally improved the fit of Tinto's model to the AI/AN data, the paths were kept in to illustrate the need to find better indicators in future research. These unexpected coefficients could be due to faulty indicators which may not be specific enough to take into account the variation in outcome that may be attributable to the type of degree being pursued, type of college going behavior among AI/ANs or type of institution attended. This suggests a need to "build down from national representative longitudinal studies to incorporate more representative student longitudinal studies at the campus level (or tribal level) . . . to address the challenges related to minority student achievement in higher education that we currently can do little more than describe" (Pavel & Reiser, 1991, p. 18).

Using Tinto's model of institutional departure, longitudinal data drawn from sophomore and senior cohorts in the High School and Beyond study, and the statistical technique known as structural equation modeling, the present study sought to provide examples of certain theoretical and methodological issues that arise when studying American Indian and Alaska Native postsecondary departure. A variation of structural equation modeling that treats all constructs as observed variables was used because of the small sample size. An initial confirmatory analysis found a weak fit between the Tinto model and the AI/AN sophomore cohort data. However, during an exploratory analysis, minor revisions to the model suggest that family background, postsecondary intentions (both prior to and during college), and formal and informal academic integration are the most significant aspects of Tinto's model that influence AI/AN postsecondary outcomes. In addition, important aspects of the Tinto model for the sophomore cohort only included the effects of academic skills, personal abilities, and prior schooling on initial postsecondary intentions. A confirmatory analysis using AI/AN senior cohort data found that initial postsecondary intentions and goal commitment are important factors that influence academic integration. These findings support existing research calling for more programs that foster positive family support and postsecondary intentions early in an AI/AN student's high school experience. Further, it was stressed that support programs should be in place to enhance academic and social integration while AI/ANs are in college. Finally, it was recommended that the sample size of AI/ANs in national data bases like HS&B need to be increased and the indicators need to be improved so that in the future better research can be conducted on American Indian and Alaska Native postsecondary outcomes.