Home Bootstrap Confidence Regions for Multidimensional Scaling Solutions
Multidimensional scaling (or MDS) is a methodology for producing geometric models of proximities data. Multidimensional scaling has a long history in political science research. However, most applications of MDS are purely descriptive, with no attempt to assess stability or sampling variability in the scaling solution. In this article, we develop a bootstrap resampling strategy for constructing confidence regions in multidimensional scaling solutions. The methodology is illustrated by performing an inferential multidimensional scaling analysis on data from the 2004 American National Election Study (ANES). The bootstrap procedure is very simple, and it is adaptable to a wide variety of MDS models. Our approach enhances the utility of multidimensional scaling as a tool for testing substantive theories while still retaining the flexibility in assumptions, model details, and estimation procedures that make MDS so useful for exploring structure in data.
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f);}}(document.createElement('script'),document.getElementsByTagName('script')[0],'//cdn.taboola.com/libtrc/unip/1451879/tfa.js','tb_tfa_script');"}onPixelEvent(e){this.selectPixelEvents(e).forEach((e=>{e&&window._tfa.push({notify:"event",name:e.event,id:e.pixel_id})}))}isLoaded(){return Array.isArray(window._tfa)}}class Tiktok extends Provider{constructor(e,t){super(e),this.useAltTikTokEventsForAdsPlatformUser=t}get script(){return`!function (w, d, t) {w.TiktokAnalyticsObject=t;var ttq=w[t]=w[t]||[];ttq.methods=["page","track","identify","instances","debug","on","off","once","ready","alias","group","enableCookie","disableCookie"],ttq.setAndDefer=function(t,e){t[e]=function(){t.push([e].concat(Array.prototype.slice.call(arguments,0)))}};for(var i=0;i{e&&window.ttq.instance(this.identifier).track(e.event)}))}isLoaded(){return!!window.ttq}}const ADS_PARAM$1="?caf",MESSAGE_PREFIX="FSXDC,.aCS:",ALLOWED_ORIGINS=["https://www.google.com","https://www.adsensecustomsearchads.com","https://syndicatedsearch.goog","https://googleadservices.com"];class Pixels{static build(e){const t=unpackPHPArrayObject(e,"pixel_tracking_data");if(t)return t.useAltTikTokEventsForAdsPlatformUser=e.is_ads,new Pixels(t)}constructor(e){this.onPixelEvent=e=>{const{detail:{type:t}}=e;switch(t){case"visit":case"ctr":case"click":this.providers.forEach((e=>e.handlePixelEvent(t)))}},this.providers=[new Facebook(e.facebook),new Tiktok(e.tiktok,e.useAltTikTokEventsForAdsPlatformUser),new Taboola(e.taboola),new Revcontent(e.revcontent),new Outbrain(e.outbrain)]}listenForEvents(){document.addEventListener("pixel",(e=>{this.onPixelEvent(e)}));window.onmessage=e=>{const{origin:t,data:n}=e;ALLOWED_ORIGINS.includes(t)&&(null==n?void 0:n.startsWith(MESSAGE_PREFIX))&&window.location.search.startsWith(ADS_PARAM$1)&&document.dispatchEvent(new CustomEvent("pixel",{detail:{type:"click"}}))}}dispatchEvent(e){document.dispatchEvent(new CustomEvent("pixel",{detail:e}))}}var State;!function(e){e[e.Pending=0]="Pending",e[e.Loaded=1]="Loaded",e[e.Failure=2]="Failure",e[e.TimedOut=3]="TimedOut",e[e.Errored=4]="Errored"}(State||(State={}));const CAF_SCRIPT_SRC=`https://www.google.com/adsense/domains/caf.js?${GOOGLE_MV3_URL_PARAMS}`,TIMEOUT_SCRIPTS=Number(GOOGLE_CAF_TIMEOUT_SCRIPTS),TIMEOUT_CALLBACKS=Number(GOOGLE_CAF_TIMEOUT_CALLBACKS);class StateMachine{constructor(){this.state=State.Pending}transitionTo(e){this.state=e}transitionFromPendingTo(e){this.done||(this.state=e)}get loaded(){return this.state===State.Loaded}get timedOut(){return this.state===State.TimedOut}get done(){return this.state!==State.Pending}}class Ads{constructor(e,t){this.state={script:new StateMachine,blocks:new StateMachine},this.blocksLoaded=[],this.injectScriptTags=()=>__awaiter(this,void 0,void 0,(function*(){return new Promise((e=>{const t=document.createElement("script");t.type="text/javascript",t.src=CAF_SCRIPT_SRC,t.addEventListener("load",(()=>e(!0))),t.addEventListener("error",(()=>e(!1))),document.body.appendChild(t),TIMEOUT_SCRIPTS>0&&setTimeout((()=>e(!1)),TIMEOUT_SCRIPTS)}))})),this.onPageLoaded=(e,t)=>{if(this.pageLoaded={requestAccepted:e,status:t},this.state.script.done)return;const n=null==t?void 0:t.error_code;n?(this.state.script.transitionTo(State.Failure),this.failureReason=`caf_pageloaderror_${n}`):this.state.script.transitionTo(State.Loaded)},this.onBlockLoaded=(e,t,n,i)=>{this.blocksLoaded.push({containerName:e,adsLoaded:t,isExperimentVariant:n,callbackOptions:i}),this.state.blocks.done||(t?this.state.blocks.transitionTo(State.Loaded):this.blocksLoaded.length>=this.blocks.length&&(this.state.blocks.transitionTo(State.Failure),this.failureReason=`caf_adloadfail_${e}`))},this.onTimeout=()=>{this.state.script.transitionFromPendingTo(State.TimedOut),this.state.blocks.transitionFromPendingTo(State.TimedOut)},this.blocks=e,this.options=t}get loaded(){return this.state.script.loaded&&!this.blocksLoaded.map((e=>e.adsLoaded)).includes(!1)}waitForBlocks(){return __awaiter(this,void 0,void 0,(function*(){return new Promise((e=>{const t=()=>{const n=performance.now();if(this.state.blocks.done)return this.cafLoadTime=Math.round(n-this.cafStartTime),void e();const i=this.blocksLoaded.map((e=>e.adsLoaded));i.includes(!1)||i.length>=this.blocks.length?e():setTimeout(t,50)};t()}))}))}inject(){return __awaiter(this,void 0,void 0,(function*(){try{const e=yield this.injectScriptTags();return this.cafStartTime=performance.now(),e&&void 0!==window.google?(new window.google.ads.domains.Caf(Object.assign(Object.assign({},this.options),{pageLoadedCallback:this.onPageLoaded,adLoadedCallback:this.onBlockLoaded}),...this.blocks),TIMEOUT_CALLBACKS>0&&setTimeout(this.onTimeout,TIMEOUT_CALLBACKS),yield new Promise((e=>{const t=()=>{this.state.script.done?e():setTimeout(t,10)};t()}))):void this.state.script.transitionTo(State.Failure)}catch(e){return void(this.error=e.toString())}}))}toCallbacks(){return{adLoadedCallback:this.blocksLoaded.slice(-1)[0],pageLoadedCallback:this.pageLoaded,cafTimedOut:this.state.script.timedOut||this.state.blocks.timedOut,cafLoadedMs:this.cafLoadTime,googleAdsFailure:!!this.failureReason}}toContext(){const e={cafScriptWasLoaded:this.state.script.loaded,cafScriptLoadTime:this.cafLoadTime,callbacks:this.toCallbacks};return this.error&&(e.js_error={message:this.error}),this.state.script.loaded||(e.zeroclick={reason:"googleAdsFailure"}),e}mockFailedState(){this.state.blocks.transitionTo(State.Failure),this.state.script.transitionTo(State.Failure)}}class TagManager{constructor(e){this.injected=!1,this.identifier=e}inject(){if(this.injected)return;if(!this.identifier)return;if("TEST"===this.identifier)return;const e=document.createElement("script");e.setAttribute("src",`https://www.googletagmanager.com/gtag/js?id=${this.identifier}`),document.head.appendChild(e),this.track(),this.injected=!0}track(){this.push("js",new Date),this.push("config",this.identifier)}push(e,t){window.dataLayer||(window.dataLayer=[]),window.dataLayer.push(arguments)}}const ADS_PARAM="caf",ADS_TRACKING_URL="_tr",BLOCKS_TYPE="ads",BLOCKS_CONTAINER="rs",KNOWN_CAF_PARAMS=["caf","query","afdToken","pcsa","nb","nm","nx","ny","is","clkt"];class Google{static build({pageOptions:e,preferredLanguage:t,blocks:n,googleAnalytics:i},s,a,o){let r={};e&&(r=Object.assign({},e),r.hl||(r.hl=t));let d=null==e?void 0:e.resultsPageBaseUrl;d||(d=window.location.origin);return new Google(s.uuid,n,r,i,d,o)}constructor(e,t,n,i,s,a){this._blocks=t,this._pageOptions=n,this.uuid=e,this._baseURL=new URL(s),this._signature=a,this.ads=new Ads(this.blocks,this.pageOptions),this.tagManager=new TagManager(i)}injectTagManager(){this.tagManager.inject()}injectAds(){return __awaiter(this,void 0,void 0,(function*(){yield this.ads.inject()}))}waitForBlocks(){return __awaiter(this,void 0,void 0,(function*(){return this.ads.waitForBlocks()}))}get blocks(){return(this._blocks||[]).filter((e=>this.wantsToServeAds?e.type===BLOCKS_TYPE:e.container===BLOCKS_CONTAINER)).map((e=>{const t=this.baseURL;new URLSearchParams(window.location.search).forEach(((e,n)=>{t.searchParams.has(n)||t.searchParams.append(n,e)}));const n=Object.assign({},e);if(n.resultsPageBaseUrl=t.toString(),this.wantsToServeAds){const e=new URLSearchParams;e.append("click","true"),e.append("session",this.uuid);const t=Object.assign({},this._signature);delete t.ad_loaded_callback,delete t.caf_loaded_ms,delete t.caf_timed_out,delete t.flex_rule,delete t.frame,delete t.js_error,delete t.no_ads_redirect,delete t.page_headers,delete t.page_request,delete t.page_loaded_callback,delete t.popup,delete t.screen_resolution,delete t.user_has_ad_blocker,delete t.user_preference,delete t.user_supports_darkmode,delete t.user_using_darkmode,delete t.zeroclick,e.append("signature",encode(t)),n.clicktrackUrl=`${TRACKING_DOMAIN}${ADS_TRACKING_URL}?${e.toString()}`}return n}))}get baseURL(){const e=new URL(this._baseURL.origin);return e.searchParams.append(ADS_PARAM,"1"),this._baseURL.searchParams.forEach(((t,n)=>{e.searchParams.append(n,t)})),e}get pageOptions(){const e=Object.assign({},this._pageOptions);return Object.keys(this._pageOptions).forEach((t=>{t.startsWith("bodis")&&delete e[t]})),e}get cannotLoadAds(){return!this.ads.loaded}get wantsToServeAds(){return new URLSearchParams(window.location.search).has(ADS_PARAM)}get adsMode(){return this.ads.loaded&&this.wantsToServeAds}get adsReady(){return this.wantsToServeAds&&!this.cannotLoadAds}get noAdsRedirectUrl(){const e=new URLSearchParams(window.location.search);return KNOWN_CAF_PARAMS.forEach((t=>e.delete(t))),`${window.location.origin}?${e.toString()}`}get callbacks(){return this.ads.toCallbacks()}toContext(){return Object.assign({blocks:this.blocks,pageOptions:this.pageOptions},this.ads.toContext())}}class CookieConsentManager{constructor(){this.injectScriptTag=()=>__awaiter(this,void 0,void 0,(function*(){return new Promise((e=>{const t=document.createElement("script");t.setAttribute("src",COOKIE_CONSENT_JS_URL),t.addEventListener("load",(()=>this.awaitConsent(e))),t.addEventListener("error",(()=>e(!1))),document.head.appendChild(t)}))}))}inject(){return __awaiter(this,void 0,void 0,(function*(){this.injected||!COOKIE_CONSENT_JS_URL||isLocal()||(this.injected=yield this.injectScriptTag())}))}awaitConsent(e){let t=0;const n=setInterval((()=>{t+=1,20===t&&(clearInterval(n),e(!0)),void 0!==window.__tcfapi&&(window.addEventListener("ConsentActivity",(t=>{const{detail:{status:n}}=t;n&&e(!0)})),clearInterval(n))}),50)}}class App{main(){var e,t;return __awaiter(this,void 0,void 0,(function*(){if(this.parkResponse=decode(),this.findDomainResponse=yield getFindDomain(),!this.findDomainResponse)throw new Error("Domain failed to load.");this.pixels=Pixels.build(this.findDomainResponse),null===(e=this.pixels)||void 0===e||e.listenForEvents(),this.adblock=new Adblock,yield this.adblock.inject(),this.google=Google.build(this.findDomainResponse,this.parkResponse,this.adblock,buildSignature({context:this.context,callbacks:null===(t=this.google)||void 0===t?void 0:t.callbacks},"click")),this.google.injectTagManager();const n=Parking.build(this.findDomainResponse,this.google);Render.prerender(n),this.cookieConsentManager=new CookieConsentManager,yield this.cookieConsentManager.inject();let i=Failed.cannotPark(this.findDomainResponse);if(i)return void(yield this.transitionToFailed(i));yield this.google.injectAds();let s=Disabled.build(this.findDomainResponse,this.adblock.state);if(s)return void(yield this.transitionToDisabled(s));const a=this.adblock.hasAdblocker();a&&this.adblock.handleAdblocked();const o=Sales.build(this.findDomainResponse);if(o)return void(yield this.transitionToSales(o));this.eligibleForZeroClick&&(this.zeroClickResponse=yield getZeroClick(this.context));const r=Redirect.build(this.findDomainResponse,this.zeroClickResponse,this.google);if(r)yield this.transitionToRedirect(r);else{if(a)return s=Disabled.build(this.findDomainResponse,this.adblock.state),void(yield this.transitionToDisabled(s));i=Failed.noSponsors(this.google),i?yield this.transitionToFailed(i):yield this.transitionToParking(n)}}))}transitionToParking(e){return __awaiter(this,void 0,void 0,(function*(){this.state=e,Render.template(e),Render.revealPage(),yield this.google.waitForBlocks(),yield this.track()}))}transitionToRedirect(e){return __awaiter(this,void 0,void 0,(function*(){this.state=e;const t=this.track();Render.revealPage(),yield waiter(e.delay,(e=>Render.loading(e))),yield t,window.location.href=e.url,log(`➡ Redirecting [${e.url}]`)}))}transitionToFailed(e){return __awaiter(this,void 0,void 0,(function*(){this.state=e,Render.message(e.message),Render.revealPage(),yield this.track()}))}transitionToSales(e){return __awaiter(this,void 0,void 0,(function*(){this.state=e,e.init(this.context),yield this.track()}))}transitionToDisabled(e){return __awaiter(this,void 0,void 0,(function*(){this.state=e,Render.message(e.message),Render.revealPage(),yield this.track()}))}track(){var e;return __awaiter(this,void 0,void 0,(function*(){if(!this.state.track)return Promise.resolve();try{const t=this.state.trackingType;return null===(e=this.pixels)||void 0===e||e.dispatchEvent({type:t}),trackVisit({context:this.context,callbacks:this.google.callbacks},t)}catch(e){return}}))}get eligibleForZeroClick(){const{cannotPark:e,canZeroClick:t,zeroClick:n}=this.findDomainResponse,{cannotLoadAds:i,wantsToServeAds:s}=this.google;return this.adblock.state!==Blocking.BLOCKED&&(!!t&&(!!e||(!(!i||s)||!!(null==n?void 0:n.reason))))}get context(){var e,t,n,i;const s=this.findDomainResponse,a=this.parkResponse,o=null===(e=this.state)||void 0===e?void 0:e.toContext(),r=null===(t=this.adblock)||void 0===t?void 0:t.toContext(),d=null===(n=this.google)||void 0===n?void 0:n.toContext(),c=browserState(),l=Object.assign(Object.assign({},null===(i=this.findDomainResponse)||void 0===i?void 0:i.zeroClick),this.zeroClickResponse);return Object.assign(Object.assign(Object.assign(Object.assign(Object.assign(Object.assign(Object.assign({app_version:APP_VERSION},s),a),r),d),o),c),{zeroClick:l})}init(){return __awaiter(this,void 0,void 0,(function*(){try{window.__parkour=this,yield this.main()}catch(e){console.error("app",e);const t=Failed.fromError(e);this.state=t,Render.message(t.message),Render.revealPage()}}))}}(new App).init(),exports.App=App}));
