Using the Linear Logistic Test Model to Investigate a Discourse-based Model of Reading Comprehension

S. L. Latimer
Royal Australian Navy

This study applies the Linear Logistic Test Model (LLTM) to examine the validity of a reading mechanism proposed by Kintsch. This mechanism is based on individual cognitive operations and semantic structures in the reading material. The LLTM analysis indicated that the assumed cognitive operations by which readers establish a coherent representation of semantic structure accounted for most of the variation in the processing difficulty of the experimental materials. It was concluded that with added constraints, Kintsch's model may provide a useful simulation of the comprehension process and, further, that the LLTM is a valuable investigative tool in this area.

INTRODUCTION

The comprehension and memorization of prose is a problem which has recently become a major concern in psychology. Before the 1970s, cognitive psychologists confined their interest to the processing and memorization of unrelated words and sentences. Research into the comprehension of connected discourse was the domain of the educators. However, the early 1970s brought the development of text grammars in linguistics and of artificial intelligence models in computer science. Both provided an impetus for psychologists to return to this area of human experience and several theories about the comprehension and memorization of prose have been developed.

Amongst the theorists who emphasize the semantic and pragmatic aspects of the comprehension process are those who argue that a complete understanding of this problem requires some scheme by which the semantic structure of the text is analyzed. Some of these writers are concerned with meaning at the individual idea or microstructure level (viz., Crothers, 1972; Frederiksen, 1972, 1975a, 1975b, 1975c; Kintsch, 1974; Meyer, 1975) while others deal with the global organization or macrostructure of prose (viz., Rumelhart, 1975; Thorndyke, 1977).

However, these text-structure theorists do not attempt to describe the cognitive mechanisms by which prose is parsed and organized in memory. Consequently, their models can be no more than descriptive.

In contrast, a model which does emphasize the cognitive processes involved in comprehension has been developed by Kintsch and Van Dijk (1978). They build upon their earlier work with microstructure (Kintsch, 1974) and macrostructure (van Dijk, 1977; van Dijk and Kintsch, 1977), their stated aim being 'to describe the system of mental operations that underlie the processes occurring in text comprehension and in the production of recall and summarization protocols' (Kintsch and van Dijk, 1978: 363). Three sets of cognitive operations are specified: one organizes the meaning elements into a coherent whole; another condenses the full meaning into the gist; and the third generates new text from the stored representation resulting from the comprehension process.

The purpose here is to investigate the validity of this description. To examine all of the processing assumptions, however, would be impracticable. Therefore, only the coherence mechanism by which the meaning units expressed in the semantic structure are processed and organized in memory is our concern. This component is easily isolated from the total comprehension process; further, in being the first stage of that process, it is a logical starting point.

The wider study from which this paper originates investigated the degree to which comprehensibility is 'the result of the interaction between a particular text (with its text characteristics) and particular readers (with their information-processing characteristics) ' (Kintsch and Vipond, 1979: 362). The substantive hypothesis was that the difference between better and poorer readers on measures of reading time and reading comprehension tasks, when administered a relatively incoherent text, will be greater than the difference between these reader types when administered a relatively coherent text. An additional test of the proposed reading mechanisms in relation to the relative coherence of texts was also conducted using the Linear Logistic Test Model (LLTM) and it is this analysis which is of interest here.

Before proceeding to an account of the LLTM and its application, it is necessary first to provide a brief description of Kintsch's coherence mechanism.

THE COHERENCE MECHANISM

The elements of Kintsch's analysis are word concepts which are essentially 'lexical entries expressed linguistically through a word' (Kintsch, 1974: 12). Propositions `are n-tuples of word concepts, one of which serves as a predicator and the other as arguments' (Kintsch, 1974: 12). Predicates or relations are normally expressed in English as verbs, adjectives or conjunctions, whereas arguments are usually expressed by nouns. To illustrate, consider (1) below:

Mary bakes a cake. (BAKE, MARY, CAKE) (1)

The sentence is represented by the proposition enclosed in the parentheses within which the predicate is always written first followed by one or more arguments. Note that the word concepts are denoted by words in capital letters and all the terms are separated by commas.

Propositions do not normally stand alone. Instead, they stand in relation to each other and so form a text base. Within this text base or ordered list of propositions, a particular word concept may be an argument in more than one proposition. In this situation, the proposition containing the repeated argument is 'said to be subordinated to the proposition where the argument originally appeared', (Kintsch, 1974: 16). These subordination relationships constitute the hierarchical structure of text which can be represented graphically. Table I exemplifies a formal representation of such a structure.

TABLE I
ENGLISH BUCCANEERS PASSAGE - LOW COHERENCE VERSION TEXT
ENGLISH BUCCANEERS
The eighteenth century was very rich in voyages of exploration. One of the reasons for this was because the English buccaneers made a number of remarkable voyages round the world at the beginning of the eighteenth century. Spanish ships were captured and Spanish towns were held up to ransom. Men adventured into the Pacific, which most of them reached by sailing round Cape Horn, in search of these. After spending a year or eighteen months on the west coast of South America, the buccaneers returned to England across the Pacific and Indian Oceans and round the Cape of Good Hope.
TEXT BASE COHERENCE GRAPH
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
(ENGLISH, BUCCANEERS)
(WAS, 18TH CENTURY, RICH)
(VERY, RICH)
(IN, 2, VOYAGES)
(OF, VOYAGES, EXPLORATION)
(ONE OF, REASONS)
(REASONS, 2)
(BECAUSE, 9, 7)
(MADE, 1, VOYAGES)
(NUMBER, VOYAGES)
(REMARKABLE, VOYAGES)
(LOC: ROUND, VOYAGES)
(TIME: AT, VOYAGES, 18TH CENTURY)
(BEGINNING, 18TH CENTURY)
(SPANISH, SHIPS)
(WERE, 15, CAPTURED)
(AND, SHIPS, TOWNS)
(SPANISH, TOWNS)
(HELD UP, 18, RANSOM)
(ADVENTURED, MEN)
(LOC: INTO, 20, PACIFIC)
(MOST, MEN)
(REACHED, 22, PACIFIC)
(BY, 23, 25)
(ROUND, SAILING, CAPE HORN)
(IN SEARCH, 20, 17)
(TIME: AFTER, 28)
(SPEND, BUCCANEERS, 29)
(OR, YEAR, EIGHTEEN MONTHS)
(LOC: ON, 28, COAST)
(WEST, COAST)
(OF, COAST, SOUTH AMERICA)
(RETURNED, BUCCANEERS, ENGLAND)
(ACROSS, 33, OCEANS)
(PACIFIC, OCEAN)
(INDIAN, OCEAN)
(ROUND, 33, CAPE OF GOOD HOPE)
taxonomy

Argument repetition is important in text coherence, because it relates new information to information already processed. Kintsch (1978: 59) suggests that a connection among the propositions of the text base is established when all of the propositions have one or more arguments in common with at least one other proposition. This connection `is not a sufficient condition for the coherence of a text base, but it is a necessary condition' (Kintsch, 1978: 59).

The critical assumption in Kintsch's coherence mechanism is that the reader attempts to represent the text in memory by a single network in which the propositions are organized hierarchically. As outlined in Kintsch and Vipond (1979: 344-54), a number of assumptions are made concerning the cognitive operations by which this representation is constructed.

The first of these is that, because of capacity limitations, a reader establishes this memorial representation in cycles. That is, the reader processes a portion of the text base, connects it to a growing graph and continues on to the next section. The number of propositions processed in each cycle is in part determined by the text through the sentence and phrase boundaries. However, the size of this input set is also a reader characteristic which limits the number of propositions that are worked in parallel. This number will be denoted by `n'. Because it is also assumed that individuals differ in their short-term or working memory capacity, the size of `n' will vary among readers.

The second processing assumption is that a reader will attempt to maintain coherence between successive input sets by selecting a subgraph from each cycle. Then this subgraph is retained in short-term memory (STM) and connected through argument repetition to the new incoming section of the text base. Those propositions contained in the input set which are not selected and retained in STM are stored in long-term memory (LTM). This subgraph or STM set, being part of working memory, is seen as some kind of STM memory buffer. The size of this buffer will be denoted by `s'. It is argued that this buffer capacity is a source of individual differences in reading comprehension.

Given that memory limitations prevent the entire graph being carried along in STM, the next model assumption specifies which propositions in the cycle are retained in the buffer. Kintsch intuitively suggests a selection strategy which favors the most important as well as the most recent propositions. This he calls the 'leading-edge rule'.

The fourth assumption is that if no connection is found between the input set and the STM set, a search of LTM is made in order to determine if a proposition already stored can provide the necessary connection between the new information and the existing network. If such a proposition is located in LTM then it is reinstated in working memory; when a number of connective propositions are available, only the most recent is reinstated. If an overlap proposition however cannot be found, then the reader must infer as many additional propositions as required to provide a connection.

Even if the text base is processed in a number of connected subgraphs, the resulting structure may differ from the `ideal' coherence graph which is constructed as if readers have no memory limitations. For example, a proposition (and the whole subgraph subordinated to it) may be annexed to a proposition far down in the graph during processing, but when the whole graph becomes available, a connection to a higher level proposition is found. As a result the reader is assumed to reorganize his/her memory representation so that it becomes more like the `ideal' network.

In summary, the model characterizes the difficulty by which text is comprehended in terms of the number of cycles, reinstatements, inferences, and reorganizations required to construct the `ideal' network in memory. The demand placed on these microprocessors is not only a function of the coherence of the text base but further depends on the working memory capacity of the reader.

THE LINEAR LOGISTIC TEST MODEL

The LLTM is a generalization of the Rasch's simple logistic model (SLM) for responses to dichotomously scored test items (Rasch, 1966). One form of this model, which indicates the probability of a correct response is given by:

Rasch dichotomous model (2)

where βv = ability parameter of subject v, v = 1, 2_ . ., n,
δi = difficulty parameter of item i, i = 1, 2, . . ., k, and
+ = a correct response.

That is, according to the SLM, the probability that subject v solves item i correctly is a logistic function of βv, which characterizes the ability of the subject, and δi, which characterize the difficulty of the item. These two parameters can be estimated using conditional maximum likelihood (CMLE) procedures.

The LLTM, developed by Fischer (1973, 1976, 1977) and Spada (1977), extends the basic Rasch model to incorporate assumptions about the cognitive operations involved in solving items. In particular, it assumes that the item difficulty is itself `a linear function of the number and difficulty of the necessary operations' (Spada, 1977: 241). This linear combination is presented in (3):

difficulty decomposition (3)

where ηj = basic parameters attached to the cognitive operation j,
qij = weight of operation j in item i (e.g., the hypothetical frequency with which operation j is needed in item i), and
c = a normalizing constant.

Substituting (3) into (2) gives the usual characterization of the LLTM:

linear logistic test model (4)

The basic parameters ηj can be estimated again using CMLE methods.

The validity of the LLTM, and hence of the hypothesized cognitive operations or task structures, can be tested by comparing the basic SLM estimates of the item difficulties (δi) with those (δi*) recovered from the CML estimates of the basic parameter difficulties ηj. This comparison can be made graphically by plotting the estimates δi against δi*b; on a co-ordinate system. Alternatively, the comparison can be made more formally by computing the correlation between δi and δi*. A further even more formal comparison can be made using a likelihood-ratio test.

The LLTM can readily be applied to the current experimental problem because specifying the number of times that each of the four coherence operations are used to construct the 'ideal' network effectively is the hypothesis of the 'psychological structure' of the reading task. As defined by Spada (1977: 228), the psychological structures of a task are 'the type and number of cognitive operations ... which enable persons of a certain population . . . to solve the task.' With regard to Kintsch's coherence mechanism, these cognitive operations are the coherence operations carried out by a given type of reader when processing the text base of a particular passage. The construction of the 'ideal' network is reflected, then, by the correctness of answers to questions about the text.

The use of the LLTM should provide a powerful test of the cognitive operations in the reading of a text as proposed by Kintsch. The empirical study in which such a test was conducted is outlined next.

THE STUDY

Subjects

The subjects are two hundred naval trainees (all males) with an average age of 16 years, 6 months.

The sample of readers was divided at the median into two groups, a 'better readers' group and a 'poorer readers' group. This division was made on the basis of scores on the reading comprehension component of the Co-operative Reading Comprehension Test, Form L (ACER, 1973). The mean raw score for the group of poorer readers was 22.16, and this corresponded to the 25th centile in the norming sample of 16-year-old South Australians. The mean raw score for the group of better readers was 36.81, and this corresponded to the 85th centile rank in the same norming sample.

On the basis of the values of 's' and 'n' considered by Kintsch (Kintsch and van Dijk, 1978; Kintsch and Vipond, 1979), the following assumptions were made about the working memory characteristics of each reader type. The poorer readers were seen to extract no more than ten propositions in each cycle; if a sentence contained more than ten propositions, the input set stopped at the nearest phrase boundary. When the sentence boundary was encountered before n was exceeded, the extraction finished there. But if the sentence contained less than four propositions, these readers continued to extract propositions expressed in the next sentence as part of the same input set. It was expected that the poorer readers' STM set was limited to three propositions which they selected according to the 'leading-edge' rule. In contrast, the better readers were assumed to process no more than fifteen propositions in each input chunk. Again, if the sentence contained more propositions, extraction ended at the next phrase boundary, whereas if it contained less, the input set ended at the boundary. Processing was assumed to continue across the sentence boundary only if less than nine propositions had already been extracted. Again using the 'leading-edge' rule, the better readers should have selected seven propositions for the buffer.

Materials

The experimental materials were based on ten paragraphs selected from The Conquest by Sea by G. Avril (1960). This book contains descriptive prose dealing with the various events and technological developments in maritime history. Accordingly, it was expected to be of interest to a group of naval recruits. Further, the vocabulary, word, sentence and paragraph length, and grammatical complexity are such that adolescent readers should experience no decoding difficulties. It was decided to select all the materials from the one text so as to facilitate comparability between the passages in terms of surface features and writing style.

All of the 100-110-word paragraphs contained in this book of 28 chapters were coded. Ten of these paragraphs were randomly selected with the restricted condition that only one paragraph be chosen from a particular chapter. This paragraph length was specified because, as argued by Kintsch and Vipond (1979: 344), a longer text involves, in addition to the construction of a propositional text base, a macrostructure analysis. This study is not concerned with the latter analysis. Only one paragraph was selected from each chapter because the topic of a chapter establishes a macrostructure between the text base of two or more of its paragraphs. Because the topics of the chapters are diverse, it was considered that such a problem would not arise between paragraphs from different chapters.

To test the hypothesis of concern to the original broader study, two versions of each passage were constructed. This was done by the author using the text base of the original passage as a guide. One version required both reader types to carry out a number of cycles, reinstatements, inferences and reorganizations with the poorer readers requiring to make many more than the better readers. This was called the low coherence version. The other version necessitated few of these operations by either reader type and this was termed the high coherence version.

To illustrate, the low coherence version of the `English Buccaneers' passage is the one already presented in Table I. The propositional text base of this passage, which is also given in Table I, has been derived according to the procedure described in Kintsch (1974) and consists of 37 propositions which are numbered and listed according to the order in which their predicates appeared in the English text. Note that a proposition embedded as an argument of another proposition is referred to in that proposition as a number.

As explained previously, propositions are connected if they share an argument. For example, propositions two and three are connected because they both contain the argument RICH and further, propositions one and nine are connected because the former is embedded as one of the arguments of the latter. The text base is seen to be connected and therefore coherent, if there is at least one path from every proposition to every other one.

Such connections are seen more clearly in the coherence graph given in Table I. The network is headed by the proposition underlying the title of the passage, namely (ENGLISH, BUCCANEERS), and is called the superordinate proposition. This proposition is connected, first to proposition nine because it is embedded as an argument of that proposition, and secondly to proposition 33 as it, too, contains the argument BUCCANEERS. Third level propositions are connected to either proposition nine or 33 because they share an argument with them, but not with the superordinate proposition. However, proposition 20 leads a separate graph because it does not share an argument with any of the propositions in the main graph. Consequently, this text base is not coherent in itself and only becomes so if the reader makes an inference which connects propositions one and 20.

TABLE II
THE CONSTRUCTION OF THE TEXT BASE FOR ENGLISH BUCCANEERS PASSAGE - LOW COHERENCE VERSION*
POORER READERS
n<=10
a=3
BETTER READERS
n<=15
a=7
taxonomic cycle
* KEY: ( )-REINSTATEMENT #-INFERENCE []REORGANIZATION

This incoherence places those readers with a more limited working memory capacity at a distinct disadvantage. This is clearly indicated in Table II which presents the sequence of cycles by which each reader type represents the text base in memory as a coherent network.

To begin, the first sentence plus the title contains five propositions and so constitutes a processing cycle for the poorer readers. This is given as CYCLE A. The particular input set does not contain a proposition to link the title to the first sentence and an inference is required to establish a connection. As a result, propositions two to five are assigned to the wrong level in the hierarchy, as indicated by their enclosure in a box, and a reorganization will be required during a check of the entire graph. Carrying over propositions two, four and five (the STM set in each cycle is underlined), these readers continue to process the nine propositions contained in the second sentence as CYCLE B. Even though this input set includes proposition nine, which shares an argument with the superordinate proposition, the exclusion of the latter from the STM set allows annexation via the connection between propositions seven and two.

Comparison of this subgraph with the ideal network in Table I shows that the propositions are incorrectly placed. As a result, they require a further reorganization. In contrast, the specified value of `n' for the better readers allows them to process the first two sentences as one input set. Because nine, the second level proposition, is processed in the same cycle as the superordinate, CYCLE A constructs this subgraph as in the `ideal' network.

The third sentence is processed by the poorer readers in CYCLE C. Because the buffer carried over into this cycle fails to provide any connection, this sentence is annexed via an inference. This works to assign proposition 17 and its subordinates too high in the hierarchy. The poorer readers continue to process the next sentence in CYCLE D. This sentence contains proposition 26, a second level proposition connected through argument overlap to proposition 17. This latter proposition and its subordinates constitute the buffer in this cycle and are correctly subordinated to proposition 26 thus making the required reorganization during the cycle. However, the subgraph must still be annexed to the main graph. Therefore, because no link exists an LTM search is conducted which leads to the inference that `men' refers to the `English Buccaneers'. Such an inference requires first that the superordinate is reinstated in STM.

The better readers process the propositions expressed in the third and fourth sentences as shown in CYCLE B. These readers do not stop extraction at the end of the third sentence. This is because the sentence contains only five propositions and therefore they continue to process the seven propositions expressed in the next sentence. The subgraph formed is dominated by proposition 20 and is structured in accordance with the ideal network. Again, the subgraph is annexed by an inference, but because of the larger STM capacity of these readers, the subordinate proposition is still in the buffer. Accordingly they avoid the reinstatement made by the poorer group of readers.

The last eleven propositions are processed in one cycle by both the poorer and better readers. This is because `n' is only just exceeded for the former, while the greater chunking size for the latter can easily accommodate a sentence of this length. However, the poorer readers' smaller STM capacity limits the buffer to propositions 20, 22 and 23, excluding the superordinate proposition which is connected in the ideal network to 33, the leading proposition in this subgraph. Annexation, therefore, requires reinstatement of proposition one, contrasting the better readers who retain the superordinate in the buffer and so easily connect this input set to the main graph.

In summary, this text is incoherent and as such might be judged as difficult to read, especially for the readers characterized by values of small `s' and 'n'. That is, the poorer readers are required to perform five cycles, two reinstatements, three inferences and three reorganizations. The greater working memory capacity of the better readers largely overcomes this incoherent structure in that they carry out only three cycles and one inference in order to construct the `ideal' network.

As shown in Table III, the high coherence version of the `English Buccaneers' passage differs significantly from the low coherence version in that the superordinate proposition (ENGLISH, BUCCANEERS) is connected through argument overlap to all the major subgraphs constructed from the text base. Consequently, assuming no processing limitations, the `ideal' network could be constructed without making any inferences. Because of this coherence and the particular order by which the propositions are expressed in the surface structure, this text places few demands on either reader type.

TABLE III
ENGLISH BUCCANEERS PASSAGE - HIGH COHERENCE VERSION TEXT
ENGLISH BUCCANEERS
English buccaneers made a number of remarkable voyages round the world at the beginning of the eighteenth century. These voyages by the buccaneers were one of the reasons why the eighteenth century was very rich in voyages of exploration. These men adventured into the Pacific, which most of them reached by sailing round Cape Horn, in search of Spanish ships to capture and Spanish towns to hold up to ransom. After spending a year or eighteen months on the west coast of South America they returned to England across the Pacific and Indian Oceans and round the Cape of Good Hope.
TEXT BASE COHERENCE GRAPH
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
(ENGLISH, BUCCANEERS)
(MADE, 1, VOYAGES)
(NUMBER, VOYAGES)
(REMARKABLE, VOYAGES)
(LOC: ROUND, VOYAGES, WORLD)
(TIME: AT, VOYAGES, 18TH CENTURY)
(BEGINNING, 18TH CENTURY)
(WERE, 2, 9)
(ONE OF, REASONS)
(WHY, REASONS, 11)
(WAS, 18TH CENTURY, RICH)
(VERY, RICH)
(IN, RICH, VOYAGES)
(OF, VOYAGES, EXPLORATION)
(ADVENTURED, 1)
(LOC: INTO, 15, PACIFIC)
(MOST, 1)
(REACHED, 17, PACIFIC)
(BY, 18, 20)
(ROUND, SAILING, CAPE HORN)
(IN SEARCH, 15, SHIPS)
(SPANISH, SHIPS)
(TO CAPTURE, SHIPS)
(IN SEARCH, 15, TOWNS)
(SPANISH, TOWNS)
(HOLD UP, TOWNS, RANSOM)
(TIME: AFTER, 33, 28)
(SPEND, 1,29)
(OR, YEAR, EIGHTEEN MONTHS)
(LOC: ON, 28, COAST)
(WEST, COAST)
(OR, COAST, SOUTH AMERICA)
(RETURNED, 1, ENGLAND)
(ACROSS, 33, OCEANS)
(PACIFIC, OCEAN)
(INDIAN,OCEAN)
(ROUND, 33, CAPE OF GOOD HOPE
taxonomic cycle

TABLE II
THE CONSTRUCTION OF THE TEXT BASE FOR ENGLISH BUCCANEERS PASSAGE - HIGH COHERENCE VERSION*
POORER READERS
n<=10
a=3
BETTER READERS
n<=15
a= 7
taxonomic cycle

This is made explicit in Table IV which shows the text base construction carried out by the better and poorer readers. The first cycle by the poorer readers contains seven propositions which ends extraction at the sentence boundary and forms an `ideal' subgraph. CYCLE B processes the second sentence, which is expressed by nine propositions and so is more compatible with the poorer readers' input size. Because the buffer contains the superordinate proposition and its subordinate, this subgraph is easily annexed to the graph constructed so far, with all propositions being assigned their proper status.

Processing the first two sentences is even less demanding for the better readers who process all 14 propositions in one cycle. The next twelve propositions are processed by the poorer readers in CYCLE C which the readers were able to extract in one chunk. This was possible because the phrase boundary following the tenth proposition coincided with the end of the sentence. The better readers process this sentence in an identical fashion. The last sentence contains eleven propositions and is processed in one cycle by both reader types, thus completing the construction of the ideal graph. This high coherence version might therefore be described as an easy text because it requires no reinstatements, inferences or reorganizations; the only difference between the reader types is that the poorer readers must make one more cycle.

TABLE V
ENGLISH BUCCANEERS PASSAGE - ORIGINAL VERSION TEXT
One of the reasons why the eighteenth century was so rich in voyages of exploration was because at the beginning of the century there were a number of remarkable voyages round the world made by the English buccaneers. These men adventured into the Pacific in search of Spanish ships to capture and Spanish towns to hold up to ransom. Most of them reached the Pacific by sailing round Cape Horn and, after spending a year or eighteen months on the west coast of South America, returned to England across the Pacific and Indian Oceans and round the Cape of Good Hope.
TEXT BASE COHERENCE GRAPH
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
(ONE OF, 2)
(REASONS, 3)
(WAS, 18TH CENTURY, RICH)
(SO, RICH)
(IN, RICH, VOYAGES)
(OF, VOYAGES, EXPLORATION)
(BECAUSE, 2, 11)
(TIME AT, 11, 18TH CENTURY)
(BEGINNING, 18TH CENTURY)
(NUMBER, 11)
(REMARKABLE, VOYAGES)
(LOC: ROUND, 11, WORLD)
(BY, 11, BUCCANEERS)
(ENGLISH, BUCCANEERS)
(ADVENTURED, 14)
(LOC: INTO, 15, PACIFIC)
(IN SEARCH, 15, SHIPS)
(SPANISH, SHIPS)
(TO CAPTURE, SHIPS)
(IN SEARCH, 15, TOWNS)
(SPANISH, TOWNS)
(HOLD UP, TOWNS, RANSOM)
(MOST, 14)
(REACHED, 23, PACIFIC)
(BY, 24, 26)
(ROUND, SAILING, CAPE HORN)
(TIME: AFTER, 33, 28)
(SPEND, 23, 29)
(OR, YEAR, EIGHTEEN MONTHS)
(LOC: ON, 28, COAST)
(WEST, COAST)
(OF, COAST, SOUTH AMERICA)
(RETURNED, 23, ENGLAND)
(ACROSS, 33, OCEANS)
(PACIFIC, OCEAN)
(INDIAN, OCEAN)
(ROUND, 33, CAPE OF GOOD HOPE)
taxonomic cycle

As a point of interest, the original 'English Buccaneers' passage is presented in Table V along with the text base and coherence graph. Although this text is coherent in that all the major subgraphs are connected to the superordinate proposition, the lengths of the sentences contained in this passage are inappropriate to the chunking capacity of both reader types and further, the writer failed to express the important ideas at the beginning of the sentences. Presentation of the text base construction would show that this text is processed by the less able readers in four cycles, three of which involve reinstatements, and further, necessitates a reorganization during a check of the entire graph. The better readers avoid any reinstatements during the three cycles they perform. However, they are still required to carry out a reorganization. In terms of comprehensibility, then, this original passage is located somewhere between the low and high coherence versions constructed for the study.

It is important to comment briefly on the comparability of the high and low coherence versions of each passage in terms of both surface and microstructure variables. First, the passages ranged in length from 100 to 110 words across both versions and, more importantly, the largest difference between any two versions was only four words. Less uniform were the number of sentences. Some of the low coherence versions of a passage contain up to three more sentences than the high coherence counterpart. The number of propositions expressed in these texts ranged from 37 to 46, although the difference between the low and high coherence versions for each passage was no more than one. Finally, the computed Flesch (1948) reading ease (RE) scores for these passages varied between 74 and 97 suggesting that these texts should be easy to read. The RE difference between the low and high coherence versions ranged widely across the passages from one to eleven points on the readability scale. Generally, the low coherence versions had a higher Flesch score than the high coherence versions.

The Dependent Variable

According to the model under investigation, if the operations required to process the text base are not carried out, then the memorial representation is incomplete, disconnected and disorganized. Therefore, a task which attempted to disclose the failure by the readers to construct the 'ideal' network was devised.

This task required the subjects to identify a single sentence summary of each passage by distinguishing it from three alternatives which were increasingly less like the meanings conveyed by the text base. The summary and its alternatives consisted of statements representing the superordinate propositions leading the major subgraphs in the text base of the original passage. In the correct summary, these statements were related as in the ideal network by explicit connectives, even though some were only implied in the text base of the original passage. The alternatives did likewise, except that they progressively distorted these links.

The rationale behind these questions is that the correct summaries are equivalent in meaning to the passages and contain the same substantive words. Therefore, even though it contains fewer propositions, each can be processed into a representation which mirrors the structure of the 'ideal' network. When asked to choose the summary closest in meaning to the passage, readers who have carried out the required cycles, reinstatements, inferences and reorganizations will match their representation with the structure of the correct summary. Those subjects who fail to construct the 'ideal' network will, amongst other things, not form the correct links between the major subgraphs and will therefore be more likely to select one of the alternative summaries. The more disconnected the representation, the greater the chance that the reader will choose an alternative which violates most or all of the relationships within the original text base. This argument assumes that the summaries are themselves easily processed by both reader types.

To illustrate, consider the `English Buccaneers' passage given earlier. The correct summary, as presented in Table VI is constructed from the leading propositions in the text base of this passage with one or two propositions from each of the major subgraphs being included. The incorrect summaries are also shown in Table VI and while expressing the same leading proposition and their subordinates, they contain different connective propositions. Clearly, these manipulations distort the relationships within the original text base and so the meanings of these summaries deviate increasingly from that of the original passage.

These summary questions can be considered as tests of comprehension because readers cannot answer them correctly unless they have semantically encoded the passage. Objection to this might be raised in that the summaries share substantive words with the passage and so the correct summary might be identified as such by matching orthography or phonology. However, these words are common to all four alternatives which differ only in the connectives used and these were rarely taken directly from the passages; indeed on most occasions they were not even explicit in the text. Therefore, the correct summary is related by meaning and not surface feature and so must be comprehended in order to be matched with the passage.

TABLE VI
SUMMARIES OF THE ENGLISH BUCCANEERS PASSAGE*

Correct Summary

The eighteenth century was rich in voyages of exploration because of the number of remarkable voyages by the English buccaneers adventuring into the Pacific, most of whom returned to England round the Cape of Good Hope.

Incorrect Summaries

The eighteenth century was rich in voyages of exploration after a number of remarkable voyages by the English buccaneers adventuring into the Pacific, most of whom returned to England round the Cape of Good Hope.

The eighteenth century was rich in voyages of exploration after a number of remarkable voyages but the English buccaneers adventured in to the Pacific, most of whom returned to England round the Cape of Good Hope.

The eighteenth century was rich in voyages of exploration after a number of remarkable voyages but the English buccaneers adventured into the Pacific, while others returned to England round the Cape of Good Hope.

* Alternatives listed in order of increasing distortion with connectives underlined.

Design

A consequence of the design for the wider study was that the data analyzed by the LLTM were collected from four populations. One data set was provided by the better readers who were administered the high coherence versions of the first five passages (SET A) and the low coherence versions of the remaining five passages (SET B). Another data set was obtained from the poorer readers allocated this same combination of the SET A and SET B passages. The other two data sets were those for the better and poorer readers given the low coherence versions of the SET A passages and the high coherence versions of the SET B passages. Allocation of the reader types to these set combinations was random.

Procedure

The experimental passages and the summary questions were presented in a test booklet, with separate forms being constructed for the high and low coherence versions of each set. Testing took place in the regular class groupings which ranged in size from 20 to 30 students. The subjects were instructed to read each passage as quickly as possible and following the completion of another task which is not of importance here, were required to choose the summary which was closest in meaning to the passage they had just read. For the LLTM analysis, the selection of the correct summary was scored 1 while the choice of an incorrect alternative was scored 0.

Task Structure Hypotheses

The estimated difficulties of the summary questions can be decomposed into the basic parameters attached to cycles (*eta;1), reinstatements (η2), inferences (η3) and reorganizations (η4). The weight given to these operations in the summary items is the frequency by which they are carried out in order to construct the ideal network. These operation frequencies can be summarized into the task structure matrix Qkxm, where k is the number of items and m is the number of basic operations. A different matrix is required for each of the four data sets as the number of operations varies according to the type of reader and version of the passage. These frequency matrices are presented in Table VII.

RESULTS

Analysis of the responses on the summary questions according to the LLTM was carried out using the LLTM2 program. (LLTM2, Linear Logistic Test Model, Version 2. The University of Western Australia, 1980.) This routinely estimates the basic parameters ηj and their standard errors and provides the item difficulties recovered from ηj and the Q matrix. Further, the program re-runs the data to estimate the item difficulties and their standard errors according to the SLM. Lastly, a likelihood-ratio test is carried out. This test is given by (5) below:

χ2 = -2 [L - L(0)] on K-1-M degrees of freedom, (5)

where L is the log-likelihood which corresponds to δi*, and and L(0) is the loglikelihood formed from δi.

TABLE VII
TASK STRUCTURE MATRICES
PASSAGE ITEM POORER READERS
Set A-Low Coh.
Set B-High Coh.
POORER READERS
Set A-High Coh.
Set B-Low Coh.
BETTER READERS
Set A-Low Coh.
Set B-High Coh.
BETTER READERS
Set A-High Coh.
Set B-Low Coh.
  OPERATIONS *
V1 V2 V3 V4 V1 V2 V3 V4 V1 V2 V3 V4 V1 V2 V3 V4
1
2
3
4
5
6
7
8
9
10
SQ01
SQ02
SQ03
SQ04
SQ05
SQ06
SQ07
SQ08
SQ09
SQ10
7
7
8
5
5
6
5
5
5
5
2
3
2
2
2
3
3
2
2
2
4
2
4
3
2
0
0
0
0
0
2
3
3
3
4
0
0
0
0
0
5
6
5
4
4
6
7
5
7
6
0
2
2
0
0
2
3
3
3
3
1
0
1
0
1
1
2
1
2
3
0
0
0
0
0
3
3
2
3
3
4
4
4
3
3
4
4
3
4
4
0
1
0
0
2
1
1
1
1
O
3
2
3
1
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
4
3
4
3
3
4
4
3
4
3
0
0
0
0
0
1
0
1
0
2
1
0
1
0
1
1
1
0
0
1
0
0
0
0
0
2
1
1
0
1
* KEY: Vl = cycles, V2 = reinstatements, V3 = inferences, V4 = reorganizations

TABLE VIII
CHI-SQUARE GOODNESS-OF-FIT VALUES
OBTAINED FOR SUMMARY QUESTION DATA SETS
Data Set χ2(5)
Poorer Readers
Set A - Low Coherence
Set B - High Coherence
55.94*
Poorer Readers
Set A - High Coherence
Set B - Low Coherence
74.57*
Better Readers
Set A - Low Coherence
Set B - High Coherence
38.10*
Better Readers
Set A - High Coherence
Set B - Low Coherence
78.11*
* p < .05

As shown in Table VIII, the likelihood-ratio tests carried out during the LLTM analyses of the data obtained from the administration of the summary questions to the four groups yielded chi-squares all of which exceeded the critical value of χ2 = 11.07 at the 5 per cent level of confidence. Thus, the recovered item difficulties did not correspond perfectly to those estimated by the SLM.

The correlations between the recovered difficulties of the summary questions and the estimates according to the SLM within each data set are given in Table IX. Except for the correlations computed for the poorer readers who were given the SET A high coherence versions and the SET B low coherence versions, all are significantly different from zero, p < .05. That is, the t statistic computed from these coefficients exceeds the critical value of t = 1.86 on 8 degrees of freedom at the 5 per cent level of confidence.

The graphical comparison of the recovered difficulties of the summary questions with those provided by the SLM are presented in Figure 1. The most significant deviations from the null hypothesis line of a perfect correlation between these estimates will be highlighted in the discussion.

TABLE IX
CORRELATION BETWEEN
LLTM AND BASIC RASCH-MODEL DIFFICULTY ESTIMATES
OF SUMMARY QUESTIONS
Data Set Correlation
Coefficient
ta
Poorer Readers
Set A - Low Coherence
Set B - High Coherence
.793.69*
Poorer Readers
Set A - High Coherence
Set B - Low Coherence
.371.11
Better Readers
Set A - Low Coherence
Set B - High Coherence
.763.33*
Better Readers
Set A - High Coherence
Set B - Low Coherence
.622.25*
a The ratio is distributed as t with n-2 degrees of freedom,
thus t statistic
* p < .05

DISCUSSION

The likelihood-ratio tests provided by the LLTM and subsequent correlational analysis of the recovered difficulties of the summary questions and those provided by the SLM revealed that although the relationship between these parameter values was less than perfect, it was far from being zero in the majority of the data sets. That is, the hypothesized task structure matrices specified for the better and poorer readers on the SET A low coherence versions and the SET B high coherence versions, and for the better readers on the other combination of the passage versions, accounted for between 38 per cent and 62 per cent of the variance in the item difficulties. This means that these task structure hypotheses were generally valid and further that the formalization of these hypotheses in terms of the LLTM was reasonably correct. Thus, one summary question was more difficult than another if the passage to which it related required more cycles, reinstatements, inferences and reorganizations in order to be represented as in the `ideal' network. Further, the microprocessors seem to have encompassed a significant part of the difficulty associated with each of the summary questions.

FIGURE 1
GRAPHICAL COMPARISON OF LLTM AND BASIC RASCH-MODEL ESTIMATES
a. Poorer Readers
dichotomous Rasch vs. Linear logistic test model LLTM
Set A Low Coherence Versions
Set B High Coherence Versions
b. Poorer Readers
dichotomous Rasch vs. Linear logistic test model LLTM
Set A High Coherence Versions
Set B Low Coherence Versions
c. Better Readers
dichotomous Rasch vs. Linear logistic test model LLTM
Set A Low Coherence Versions
Set B High Coherence Versions
d. Better Readers
dichotomous Rasch vs. Linear logistic test model LLTM
Set A High Coherence Versions
Set B Low Coherence Versions

Some of the task structures for these data sets, however, were not valid since the relationships between the difficulty estimates recovered from the LLTM and obtained from the SLM were significantly different from unity or perfection. The graphical comparison of these estimates indicated that the most deviant task structures were those of the summary questions about passages ONE and SEVEN. The former item difficulty was most often harder than expected from the hypothesized task structure. This may have arisen from the position of the passage in the test booklets. Because the summary questions were a novel reading comprehension task and even though a warm-up passage was included, the subjects may still have been unsure about what was required at this early stage of the test. In contrast, the summary question about passage SEVEN was nearly always easier than expected from its hypothesized task structure. Because this trend was most pronounced in the data sets involving the low coherence version of passage SEVEN, it appears that the passage manipulations were particularly ineffective for this text.

The correlations between the LLTM and SLM difficulties in the remaining data set, namely the administration of the SET A high coherence versions and the SET B low coherence versions to the poorer readers, did not differ significantly from zero. This indicates that many of the task structures specified for this group were invalid. Examination of the direction of the deviations between the two estimates of the item difficulties failed to suggest any reason why this might be so.

Generally, however, these results can be taken to provide support for the assumption that the coherence operations contribute to the difficulty by which microstructure is processed. Further, the amount of variation in the difficulty of the experimental passages explained by these four operations is particularly significant when one considers the many encoding variables involved in reading comprehension which are ignored by the model of coherence.

As in the studies by Kintsch and van Dijk (1978); Kintsch and Vipond (1979), the size of the buffer and input chunks were specified only for two classes of readers, the better and poorer readers in the particular group. Had different values been chosen for a more precise grouping of reader types, the task structures hypothesized might have been shown to be more valid. It was a weakness of the design that more data was not available to permit this more precise specification of the task structure matrices.

It is necessary, therefore, to collect a more extensive set of data so that the working memory characteristics of different types of readers can be determined more precisely. The use of different strategies by which propositions are selected for the STM set must also be examined as should also the relationship between the syntactic boundaries and the processing limitations of the reader. With the added constraints provided by such investigations, Kintsch's coherence mechanism may provide a powerful simulation model for the cognitive operations by which the reader abstracts meaning from written discourse.

An important methodological implication of this study is the value of the LLTM as an investigative tool. The alternative procedure would have been to use multiple regression. There are, however, many analytic and interpretative problems associated with this technique. Particularly relevant to this study are the pitfalls of collinearity and suppression between some of the predictor variables. There is also the problem of the order by which the variables would be entered into the regression equations and, further, the resulting regression weights can change from sample to sample. Lastly, regression analysis here would involve mean performances on the dependent variables which only considers variance at the group level. The LLTM avoids all of these problems.

Of further interest is the fact that the number of coherence operations was found to be a more accurate predictor of the difficulty of the experimental passages than the computed Flesch (1948) reading ease scores. This highlights the inadequacy of this index and others like it. It would seem that readability formulae must go beyond the surface features of text and, more importantly, readability should be considered as a text-reader interaction rather than a property of the text alone.

A final implication of this study is in the process of writing, particularly in the area of instructional text. That is, if skilled and less skilled readers do process text in qualitatively different ways, it would appear that different writing styles need to be adopted for different types of readers. In fact, this investigation suggests a number of writing rules which should make the comprehension process easier, particularly for the less able readers. First, all the important information should be stated explicitly in the text. Secondly, a common element should relate the beginning of each sentence to the preceding information: Thirdly, ideas about the same concept should not be separated in the text. Finally, sentence length should not be too long nor too short.

REFERENCES

Australian Council for Educational Research, Manual for Cooperative Reading Comprehension Test (Forms L and M), Hawthorn, Victoria: 1973.

Avril, G., The Conquest of Sea, London: Burke, 1960.

Bobrow, D. G. & A. Collins (eds), Representation and Understanding: Studies in. Cognitive Science, New York: Academic Press, 1975.

Caroll, J. B. & R. O. Freedle (eds), Language Comprehension and the Acquisition of Knowledge, Washington, D.C.: Winston & Sons, 1972.

Crothers, E. J., 'Memory Structure and the Recall of Discourse', in Language Comprehension and the Acquisition of Knowledge, J. B. Caroll & R. O. Freedle (eds), Washington, D.C.: Winston & Sons, 1972, 247-83.

De Gruijter, D. & L. van der Kamp (eds), Advances in Psychological and Educational Measurement, Bern: Huber, 1976.

Dressler, W. U. (ed.), Current Trends in Textlinguistics, Berlin, New York: de Gruyter, 1977.

Estes, W. K., Handbook of Learning and Cognitive Processes 6, Hillsdale, New Jersey: Lawrence Erlbaum Associates, 1978.

Fischer, G. H., 'The linear logistic test model as an instrument in educational research', Acta Psychologica 37 (1973), 359-74.

Fischer, G. H., 'Some probabilistic models for measuring change', in Advances in Psychological and Educational Measurement, D. De Gruijter & L. van der Kamp (eds), Bern: Huber, 1976, 107-12.

Fischer, G. H., 'Linear logistic test models: Theory and application', in Structural Models of Thinking and Learning, H. Spada & W. F. Kempf (eds), Bern: Huber, 1977,203-25.

Flesch, R., 'A New Readability Yardstick', Journal of Applied Psychology 32 (1948), 221-33.

Frederiksen, C. H., 'Effects of Task-Induced Cognitive Operations on Comprehension and Memory Processes', in Language Comprehension and the Acquisition of Knowledge, J. B. Caroll & R. O. Freedle (eds), Washington, D.C.: Winston & Sons, 1972,211-45.

Frederiksen, C. H., 'Acquisition of Semantic Information from Discourse: Effects of Repeated Exposures', Journal of Verbal Learning and Verbal Behavior 14 (1975a), 158-69.

Frederiksen, C. H., 'Effects of Context--Induced Processing Operations on Semantic Information Acquired from Discourse', Cognitive Psychology 7 (1975b), 139-66.

Frederiksen, C. H., 'Representing Logical and Semantic Structure of Knowledge Acquired from Discourse', Cognitive Psychology 7 (1975), 371-458. (c)

Just, M. A. & P. A. Carpenter (eds), Cognitive Processes in Comprehension, Hillsdale, New Jersey: Lawrence Erlbaum Associates, 1977.

Kintsch, W., The Representation of Meaning in Memory. Hillsdale, New Jersey: Lawrence Erlbaum Associates, 1974.

Kintsch, W., 'Comprehension and Memory of Text', in Handbook of Learning and Cognitive Processes, Vol. 6, W. K. Estes (ed.), Hillsdale, New Jersey: Lawrence Erlbaum Associates, 1978, 57-86.

Kintsch, W. & T. A. van Dijk, 'Toward a model of text comprehension and production', Psychological Review 8 (1978), 363-94.

Kintsch, W. & D. Vipond, 'Reading comprehension and readability in educational practice and psychological theory', in Perspectives on Memory Research, L. G. Nilsson (ed.), Hillsdale, N.J.: Erlbaum, 1979, 329-66.

Meyer, B. J. F., The Organization of Prose and its Effects on Memory. Amsterdam: North-Holland Publishing Co., 1975.

Nilsson, L. G. (ed.), Perspectives on Memory Research. Hillsdale, NJ.: Erlbaum, 1979.

Rasch, G., Probabilistic Models for Some Intelligence and Attainment Tests, Chicago: University of Chicago Press, 1980.

Rumelhart, D. E., 'Notes on a Schema for Stories', in Representation and Understanding. Studies in Cognitive Science, D. G. Bobrow & A. Collins (eds), New York: Academic Press, 1975, 211-36.

Spada, H., 'Logistic models of learning and thought', in Structural Models of Thinking and Learning, H. Spada & W. F. Kempf (eds), Vienna: Huber, 1977, 227-62.

Spada, H. & W. F. Kempf (eds), Structural Models of Thinking and Learning, Vienna, Hans Huber Publishers, 1977.

Thorndyke, P. W., 'Cognitive structures in Comprehension and Memory of Narrative Discourse', Cognitive Psychology 9 (1977), 77-110.

Turner, A. & E. Greene, The Construction of a Propositional Text Base. Technical Report, University of Colorado, 1977.

van Dijk, T., 'Macro-structures and Cognition', in Cognitive Processes in Comprehension, M. Just & P. Carpenter (eds), Hillsdale, New Jersey: Lawrence Erlbaum Associates, 1977, 3-32.

van Dijk, T. & W. Kintsch, 'Cognitive Psychology and Discourse: Recalling and Summarizing Stories', in Current Trends in Textlinguistics, W. U. Dressier (ed.), Berlin, New York: de Gruyter, 1977, 61-80.

Using the Linear Logistic Test Model to Investigate a Discourse-based Model of Reading Comprehension, S. L. Latimer
Education Research and Perspectives, 9:1, 1982, 73-94.

Reproduced with permission of The Editors, The Graduate School of Education, The University of Western Australia. (Clive Whitehead, Oct. 29, 2002)

Rasch Models for Measurement in Educational and Psychological Research
Education Research and Perspectives. Vol. 9, No. 1 June 1982

Go to Top of Page
Go to Institute for Objective Measurement Page

Please help with Standard Dataset 4: Andrich Rating Scale Model



Rasch Publications
Rasch Measurement Transactions (free, online) Rasch Measurement research papers (free, online) Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch Applying the Rasch Model 3rd. Ed., Bond & Fox Best Test Design, Wright & Stone
Rating Scale Analysis, Wright & Masters Introduction to Rasch Measurement, E. Smith & R. Smith Introduction to Many-Facet Rasch Measurement, Thomas Eckes Invariant Measurement: Using Rasch Models in the Social, Behavioral, and Health Sciences, George Engelhard, Jr. Statistical Analyses for Language Testers, Rita Green
Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar Journal of Applied Measurement Rasch models for measurement, David Andrich Constructing Measures, Mark Wilson Rasch Analysis in the Human Sciences, Boone, Stave, Yale
in Spanish: Análisis de Rasch para todos, Agustín Tristán Mediciones, Posicionamientos y Diagnósticos Competitivos, Juan Ramón Oreja Rodríguez

To be emailed about new material on www.rasch.org
please enter your email address here:

I want to Subscribe: & click below
I want to Unsubscribe: & click below

Please set your SPAM filter to accept emails from Rasch.org

www.rasch.org welcomes your comments:
Please email inquiries about Rasch books to books \at/ rasch.org

Your email address (if you want us to reply):

 

FORUMRasch Measurement Forum to discuss any Rasch-related topic

Coming Rasch-related Events
March 31, 2017, Fri. Conference: 11th UK Rasch Day, Warwick, UK, www.rasch.org.uk
April 2-3, 2017, Sun.-Mon. Conference: Validity Evidence for Measurement in Mathematics Education (V-M2Ed), San Antonio, TX, Information
April 26-30, 2017, Wed.-Sun. NCME, San Antonio, TX, www.ncme.org - April 29: Ben Wright book
April 27 - May 1, 2017, Thur.-Mon. AERA, San Antonio, TX, www.aera.net
May 26 - June 23, 2017, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
June 30 - July 29, 2017, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Further Topics (E. Smith, Winsteps), www.statistics.com
July 31 - Aug. 3, 2017, Mon.-Thurs. Joint IMEKO TC1-TC7-TC13 Symposium 2017: Measurement Science challenges in Natural and Social Sciences, Rio de Janeiro, Brazil, imeko-tc7-rio.org.br
Aug. 7-9, 2017, Mon-Wed. In-person workshop and research coloquium: Effect size of family and school indexes in writing competence using TERCE data (C. Pardo, A. Atorressi, Winsteps), Bariloche Argentina. Carlos Pardo, Universidad Catòlica de Colombia
Aug. 7-9, 2017, Mon-Wed. PROMS 2017: Pacific Rim Objective Measurement Symposium, Sabah, Borneo, Malaysia, proms.promsociety.org/2017/
Aug. 10, 2017, Thurs. In-person Winsteps Training Workshop (M. Linacre, Winsteps), Sydney, Australia. www.winsteps.com/sydneyws.htm
Aug. 11 - Sept. 8, 2017, Fri.-Fri. On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets), www.statistics.com
Aug. 18-21, 2017, Fri.-Mon. IACAT 2017: International Association for Computerized Adaptive Testing, Niigata, Japan, iacat.org
Sept. 15-16, 2017, Fri.-Sat. IOMC 2017: International Outcome Measurement Conference, Chicago, jampress.org/iomc2017.htm
Oct. 13 - Nov. 10, 2017, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
Jan. 5 - Feb. 2, 2018, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
Jan. 10-16, 2018, Wed.-Tues. In-person workshop: Advanced Course in Rasch Measurement Theory and the application of RUMM2030, Perth, Australia (D. Andrich), Announcement
Jan. 17-19, 2018, Wed.-Fri. Rasch Conference: Seventh International Conference on Probabilistic Models for Measurement, Matilda Bay Club, Perth, Australia, Website
May 25 - June 22, 2018, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
June 29 - July 27, 2018, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Further Topics (E. Smith, Winsteps), www.statistics.com
Aug. 10 - Sept. 7, 2018, Fri.-Fri. On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets), www.statistics.com
Oct. 12 - Nov. 9, 2018, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
The HTML to add "Coming Rasch-related Events" to your webpage is:
<script type="text/javascript" src="http://www.rasch.org/events.txt"></script>

 

Our current URL is www.rasch.org

The URL of this page is www.rasch.org/erp6.htm