across all items. ‘Difficulty’ here means it is difficult to agree on the implementation or the importance ratings. Table 4 indicates that principals found it very difficult to agree the statement that RES_2 “School finances adequate for educational material” is implemented well. Just like only the students of highest ability can correctly answer the most difficult test questions, only the high SBM level schools would be the ones with high ratings on difficult items. In the right hand panel of Table 4, participation and autonomy variables appear at the top, with positive behavior of the principals and teachers appearing at the bottom – meaning these are the easiest variable to agree with.

|**Table 4: SBM Ratings b**|**y Princ**|**ipals: Rasch Analysis of 38 items**||
|---|---|---|---|
|**IMPLEMENTATION**|β|**IMPORTANCE**|β|
|RES_2 School finances adequate for educational material|1.01|AUT_5 Parentalparticipation in teacherperformance evaluation|1.78|
|TCH_5 Teachers have specialpedagogyrelated meetings*|0.88|PAR_2 Parentparticipation inpurchasingdecisions|1.59|
|LRG_5 School does well in regional scholastic competitions*|0.85|PAR_3 Participation from local communityassociations*|1.14|
|TCH_1 Teachers are able toget trainingtheyneed*|0.65|AUT_4 Parentalparticipation in school budget allocation|1.12|
|AUT_1 School can upgrade buildings or facilityas needed*|0.64|GOV_1 More central control/oversight of school functioning*|0.97|
|RES_4 Higher level of school budget*|0.62|LRG_5 School does well in regional scholastic competitions*|0.93|
|PAR_2 Parentparticipation inpurchasingdecisions*|0.61|GOV_2 Central authorities visit school frequently*|0.85|
|PAR_3 Participation from local communityassociations*|0.55|RES_1 Funds raised by parents to supplementgovt. budget*|0.7|
|TCH_4 Teachersprovide regular feedback toparents*|0.51|SIP_4 Extra-curricular activities like sports and music*|0.67|
|RES_3 School finances adequate for other operational exp*|0.34|PAR_4 Participation from Parents in event organization*|0.59|
|GOV_2 Central authorities visit school frequently*|0.32|AUT_1 School can upgrade buildings or facilityas needed*|0.44|
|TCH_3 Teachers have a sayinpedagogical decisions|0.31|GOV_3 School receives technical assistance from central level*|0.32|
|EQI_1 Better care for students with special needs/difficulties|0.23|AUT_6 School canget additional teachers when required*|0.21|
|PAR_5 Parent responsibilityfor child effort/attendance*|0.22|TCH_5 Teachers have specialpedagogyrelated meetings*|0.19|
|GOV_1 More central control/oversight of school functioning*|0.16|EQI_1 Better care for students with special needs/difficulties*|0.17|
|EQI_3 School feeding programs ensure no children are hungry|0.15|TCH_3 Teachers have a sayinpedagogical decisions*|0.14|
|RES_1 Funds raised by parents to supplementgovt. budget|0.09|EQI_3 School feeding programs *|0.14|
|GOV_3 School receives technical assistance from central level*|0.09|AUT_3 Financial support from localgovernment*|0.07|
|PAR_4 Participation from Parents in event organization|-0.03|AUT_2 School undertakes school basedprocurement*|0.05|
|AUT_5 Parentalparticipation in teacherperformance eval.|-0.03|PAR_1 Closer integration with school community*|0.05|
|SIP_3 School records are kept inperfect order*|-0.09|RES_3 School finances adequate for other operational exp*|0.03|
|LRG_2 All stakeholders are aware of NAT results*|-0.11|LRG_2 All stakeholders are aware of NAT results*|-0.08|
|TCH_2 Teachers are encouraged to use innovative methods|-0.19|RES_4 Higher level of school budget|-0.1|
|SIP_5 Schoolgrounds and toilets are always clean*|-0.21|PRI_1 School headprovidespedagogical feedback to teachers*|-0.16|
|PRI_2 School head harmonious relations with local authorities*|-0.23|RES_2 School finances adequate for educational material|-0.18|
|AUT_4 Parentalparticipation in school budget allocation*|-0.27|SIP_5 Schoolgrounds and toilets are always clean*|-0.51|
|AUT_3 Financial support from localgovernment*|-0.35|LRG_4 Teachers haveportfolios of student's achievements*|-0.51|
|AUT_2 School undertakes school basedprocurement*|-0.39|SIP_3 School records are kept inperfect order*|-0.73|
|SIP_1 More effective school administration*|-0.39|LRG_3 Teachers holdpreparatoryclasses for NATperformance|-0.79|
|PAR_1 Closer integration with school community*|-0.41|EQI_2 Remedial classes are held for weaker students*|-0.81|
|LRG_4 Teachers haveportfolios of student's achievements*|-0.47|SIP_1 More effective school administration|-0.93|
|AUT_6 School canget additional teachers when required*|-0.48|SIP_2 Goals in the School Improvement Plan are realistic*|-0.93|
|EQI_2 Remedial classes are held for weaker students*|-0.57|PAR_5 Parent responsibilityfor child effort/attendance*|-0.96|
|LRG_1 Deeper attention to student learningand other results*|-0.58|TCH_2 Teachers are encouraged to use innovative methods*|-0.99|
|SIP_4 Extra-curricular activities like sports and music*|-0.62|TCH_1 Teachers are able toget trainingtheyneed*|-1.02|
|PRI_1 School headprovidespedagogical feedback to teachers*|-0.83|TCH_4 Teachersprovide regular feedback toparents*|-1.08|
|LRG_3 Teachers holdpreparatoryNAT classes *|-0.88|PRI_2 School head harmonious local relations *|-1.14|
|SIP_2 Goals in the School Improvement Plan are realistic*|-1.12|LRG_1 Deeper attention to student learningand other results*|-1.24|

Table 4 difficulty measures are useful to intuitively understand the construction and the usefulness of Rasch measures of SBM. Some of the items Table 4 have been marked with an asterisk – based on the model infit mean square number generated from the Rasch analysis. This number is the ratio of the actual variance in ratings as compared to the Rasch model predicted variance in ratings, with a 16